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Refereed Journal Articles
2024
Khoshbin, Massy; Catani, Lorenzo; Leifer, Matthew
Alternative robust ways of witnessing nonclassicality in the simplest scenario Journal Article
In: Phys. Rev. A, vol. 109, no. 3, pp. 032212, 2024.
@article{Khoshbin2024,
title = {Alternative robust ways of witnessing nonclassicality in the simplest scenario},
author = {Massy Khoshbin and Lorenzo Catani and Matthew Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2024Khoshbin.pdf
https://arxiv.org/abs/2311.13474},
doi = {10.1103/PhysRevA.109.032212},
year = {2024},
date = {2024-03-14},
urldate = {2024-03-14},
journal = {Phys. Rev. A},
volume = {109},
number = {3},
pages = {032212},
abstract = {In this paper we relate notions of nonclassicality in what is known as the simplest nontrivial scenario (a prepare and measure scenario composed of four preparations and two binary-outcome tomographically complete measurements). Specifically, we relate the established method developed by Pusey [M. F. Pusey, Phys. Rev. A 98, 022112 (2018)] to witness a violation of preparation noncontextuality, that is not suitable in experiments where the operational equivalences to be tested are specified in advance, with an approach based on the notion of bounded ontological distinctness for preparations, defined by Chaturvedi and Saha [A. Chaturvedi and D. Saha, Quantum 4, 345 (2020)]. In our approach, we test bounded ontological distinctness for two particular preparations that are relevant in certain information processing tasks in that they are associated with the even and odd parity of the bits to communicate. When there exists an ontological model where this distance is preserved we talk of parity preservation. Our main result provides a noise threshold under which violating parity preservation (and so bounded ontological distinctness) agrees with the established method for witnessing preparation contextuality in the simplest nontrivial scenario. This is achieved by first relating the violation of parity preservation to the quantification of contextuality in terms of inaccessible information as developed by Marvian (I. Marvian, arXiv:2003.05984.), that we also show, given the way we quantify noise, to be more robust in witnessing contextuality than Pusey's noncontextuality inequality. As an application of our findings, we treat the case of two-bit parity-oblivious multiplexing in the presence of noise. In particular, given that we have a noise threshold below which preparation contextuality holds, we use it to establish a condition for which preparation contextuality is present in the case where the probability of success exceeds that achieved by any classical strategy.},
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pubstate = {published},
tppubtype = {article}
}
In this paper we relate notions of nonclassicality in what is known as the simplest nontrivial scenario (a prepare and measure scenario composed of four preparations and two binary-outcome tomographically complete measurements). Specifically, we relate the established method developed by Pusey [M. F. Pusey, Phys. Rev. A 98, 022112 (2018)] to witness a violation of preparation noncontextuality, that is not suitable in experiments where the operational equivalences to be tested are specified in advance, with an approach based on the notion of bounded ontological distinctness for preparations, defined by Chaturvedi and Saha [A. Chaturvedi and D. Saha, Quantum 4, 345 (2020)]. In our approach, we test bounded ontological distinctness for two particular preparations that are relevant in certain information processing tasks in that they are associated with the even and odd parity of the bits to communicate. When there exists an ontological model where this distance is preserved we talk of parity preservation. Our main result provides a noise threshold under which violating parity preservation (and so bounded ontological distinctness) agrees with the established method for witnessing preparation contextuality in the simplest nontrivial scenario. This is achieved by first relating the violation of parity preservation to the quantification of contextuality in terms of inaccessible information as developed by Marvian (I. Marvian, arXiv:2003.05984.), that we also show, given the way we quantify noise, to be more robust in witnessing contextuality than Pusey's noncontextuality inequality. As an application of our findings, we treat the case of two-bit parity-oblivious multiplexing in the presence of noise. In particular, given that we have a noise threshold below which preparation contextuality holds, we use it to establish a condition for which preparation contextuality is present in the case where the probability of success exceeds that achieved by any classical strategy.
2023
Catani, Lorenzo; Leifer, Matthew; Schmid, David; Spekkens, Robert W.
Why interference phenomena do not capture the essence of quantum theory Journal Article
In: Quantum, vol. 7, pp. 1119, 2023.
@article{Catani2023b,
title = {Why interference phenomena do not capture the essence of quantum theory},
author = {Lorenzo Catani and Matthew Leifer and David Schmid and Robert W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2023Catani1.pdf
https://arxiv.org/abs/2111.13727},
doi = {10.22331/q-2023-09-25-1119},
year = {2023},
date = {2023-09-25},
urldate = {2023-09-25},
journal = {Quantum},
volume = {7},
pages = {1119},
abstract = {Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the `toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.},
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pubstate = {published},
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}
Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the `toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.
Catani, Lorenzo; Leifer, Matthew; Scala, Giovanni; Schmid, David; Spekkens, Robert W.
Aspects of the phenomenology of interference that are genuinely nonclassical Journal Article
In: Phys. Rev. A, vol. 108, pp. 022207, 2023.
@article{Catani2023,
title = {Aspects of the phenomenology of interference that are genuinely nonclassical},
author = {Lorenzo Catani and Matthew Leifer and Giovanni Scala and David Schmid and Robert W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2023Catani2.pdf
https://arxiv.org/abs/2211.09850},
doi = {10.1103/PhysRevA.108.022207},
year = {2023},
date = {2023-08-10},
urldate = {2023-08-10},
journal = {Phys. Rev. A},
volume = {108},
pages = {022207},
abstract = {Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al., arXiv:2111.13727]. This raises the question of what other aspects of the phenomenology of interference đť‘‘đť‘ś in fact resist classical explanation. We answer this question by demonstrating that the most basic quantum wave-particle duality relation, which expresses the precise tradeoff between path distinguishability and fringe visibility, cannot be reproduced in any noncontextual model. We do this by showing that it is a specific type of uncertainty relation and then leveraging a recent result establishing that noncontextuality restricts the functional form of this uncertainty relation [Catani et al., Phys. Rev. Lett. 129, 240401 (2022)]. Finally, we discuss what sorts of interferometric experiment can demonstrate contextuality via the wave-particle duality relation.},
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Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al., arXiv:2111.13727]. This raises the question of what other aspects of the phenomenology of interference đť‘‘đť‘ś in fact resist classical explanation. We answer this question by demonstrating that the most basic quantum wave-particle duality relation, which expresses the precise tradeoff between path distinguishability and fringe visibility, cannot be reproduced in any noncontextual model. We do this by showing that it is a specific type of uncertainty relation and then leveraging a recent result establishing that noncontextuality restricts the functional form of this uncertainty relation [Catani et al., Phys. Rev. Lett. 129, 240401 (2022)]. Finally, we discuss what sorts of interferometric experiment can demonstrate contextuality via the wave-particle duality relation.
Leifer, Matthew S.
Uncertainty from the Aharonov-Vaidman identity Journal Article
In: Quantum Studies: Mathematics and Foundations, vol. 10, pp. 373-397, 2023.
@article{Leifer2023,
title = {Uncertainty from the Aharonov-Vaidman identity},
author = {Matthew S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2023Leifer-1.pdf
https://arxiv.org/abs/2301.08679},
doi = {10.1007/s40509-023-00301-8},
year = {2023},
date = {2023-04-24},
journal = {Quantum Studies: Mathematics and Foundations},
volume = {10},
pages = {373-397},
abstract = {In this article, I show how the Aharonov–Vaidman identity (AKet{psi} = left langle A right rangle Ket{psi} + Delta A Ket{psi^{perp}_A}) can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation (Delta A Delta B geq frac{1}{2} left | left langle left [ A,B right ] right rangle right |) than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations and show how the Aharonov–Vaidman identity can be used to handle propagation of uncertainty in quantum mechanics. Finally, I show how the Aharonov–Vaidman identity can be extended to mixed states and discuss how to generalize the results to the mixed case.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this article, I show how the Aharonov–Vaidman identity (AKet{psi} = left langle A right rangle Ket{psi} + Delta A Ket{psi^{perp}_A}) can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation (Delta A Delta B geq frac{1}{2} left | left langle left [ A,B right ] right rangle right |) than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations and show how the Aharonov–Vaidman identity can be used to handle propagation of uncertainty in quantum mechanics. Finally, I show how the Aharonov–Vaidman identity can be extended to mixed states and discuss how to generalize the results to the mixed case.
Catani, Lorenzo; Leifer, Matthew
A mathematical framework for operational fine tunings Journal Article
In: Quantum, vol. 7, pp. 948, 2023.
@article{Catani2023c,
title = {A mathematical framework for operational fine tunings},
author = {Lorenzo Catani and Matthew Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2023Catani3.pdf
https://arxiv.org/abs/2003.10050},
doi = {10.22331/q-2023-03-16-948},
year = {2023},
date = {2023-03-16},
journal = {Quantum},
volume = {7},
pages = {948},
abstract = {In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings – already introduced by Wood and Spekkens in [NJP,17 033002(2015)] – as the definition of an operational fine tuning does not involve any assumptions about the underlying causal structure. We show how known examples of operational fine tunings, such as Spekkens' generalized contextuality, violation of parameter independence in Bell experiment, and ontological time asymmetry, fit into our framework. We discuss the possibility of finding new fine tunings and we use the framework to shed new light on the relation between nonlocality and generalized contextuality. Although nonlocality has often been argued to be a form of contextuality, this is only true when nonlocality consists of a violation of parameter independence. We formulate our framework also in the language of category theory using the concept of functors.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings – already introduced by Wood and Spekkens in [NJP,17 033002(2015)] – as the definition of an operational fine tuning does not involve any assumptions about the underlying causal structure. We show how known examples of operational fine tunings, such as Spekkens' generalized contextuality, violation of parameter independence in Bell experiment, and ontological time asymmetry, fit into our framework. We discuss the possibility of finding new fine tunings and we use the framework to shed new light on the relation between nonlocality and generalized contextuality. Although nonlocality has often been argued to be a form of contextuality, this is only true when nonlocality consists of a violation of parameter independence. We formulate our framework also in the language of category theory using the concept of functors.
2022
Catani, Lorenzo; Leifer, Matthew; Scala, Giovanni; Schmid, David; Spekkens, Robert W.
What is Nonclassical about Uncertainty Relations? Journal Article
In: Phys. Rev. Lett., vol. 129, iss. 24, pp. 240401, 2022.
@article{Catani2022,
title = {What is Nonclassical about Uncertainty Relations?},
author = {Lorenzo Catani and Matthew Leifer and Giovanni Scala and David Schmid and Robert W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2022Catani.pdf
https://arxiv.org/abs/2207.11779},
doi = {10.1103/PhysRevLett.129.240401},
year = {2022},
date = {2022-12-09},
journal = {Phys. Rev. Lett.},
volume = {129},
issue = {24},
pages = {240401},
abstract = {Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli đť‘‹ and Pauli đť‘Ť observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli đť‘‹ and Pauli đť‘Ť observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.
2020
Leifer, Matthew; Duarte, Cristhiano
Noncontextuality inequalities from antidistinguishability Journal Article
In: Phys. Rev. A, vol. 101, iss. 6, pp. 062113, 2020.
@article{Leifer2020,
title = {Noncontextuality inequalities from antidistinguishability},
author = {Matthew Leifer and Cristhiano Duarte},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/Publications2020Leifer.pdf
https://arxiv.org/abs/2001.11485},
doi = {10.1103/PhysRevA.101.062113},
year = {2020},
date = {2020-06-24},
journal = {Phys. Rev. A},
volume = {101},
issue = {6},
pages = {062113},
abstract = {Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for the reality of the quantum state. Our main contribution here is to show that they are also noncontextuality inequalities.},
keywords = {},
pubstate = {published},
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Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for the reality of the quantum state. Our main contribution here is to show that they are also noncontextuality inequalities.
2017
Combes, Joshua; Ferrie, Christopher; Leifer, Matthew S.; Pusey, Matthew F.
Why protective measurement does not establish the reality of the quantum state Journal Article
In: Quantum Studies: Mathematics and Foundations, vol. 5, pp. 189–211, 2017.
@article{Combes:2015,
title = {Why protective measurement does not establish the reality of the quantum state},
author = {Joshua Combes and Christopher Ferrie and Matthew S. Leifer and Matthew F. Pusey},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/Combes2017.pdf
https://arxiv.org/abs/1509.08893},
doi = {10.1007/s40509-017-0111-4},
year = {2017},
date = {2017-07-14},
urldate = {2015-01-01},
journal = {Quantum Studies: Mathematics and Foundations},
volume = {5},
pages = {189–211},
abstract = {“Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “psi-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.},
keywords = {},
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“Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “psi-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.
Leifer, Matthew S.; Pusey, Matthew F.
Is a time symmetric interpretation of quantum theory possible without retrocausality Journal Article
In: Proc. Roy. Soc. A, vol. 473, pp. 20160607, 2017.
@article{Leifer:2017,
title = {Is a time symmetric interpretation of quantum theory possible without retrocausality},
author = {Matthew S. Leifer and Matthew F. Pusey},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/Publications2017Leifer.pdf
https://arxiv.org/abs/1607.07871},
doi = {https://doi.org/10.1098/rspa.2016.0607},
year = {2017},
date = {2017-06-21},
urldate = {2017-06-21},
journal = {Proc. Roy. Soc. A},
volume = {473},
pages = {20160607},
abstract = {Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called lambda-mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.},
keywords = {},
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Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called lambda-mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.
2015
Jennings, David; Leifer, Matthew
No return to classical reality Journal Article
In: Contemporary Physics, vol. 57, pp. 60–82, 2015.
@article{Jennings2015,
title = {No return to classical reality},
author = {David Jennings and Matthew Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/jennings2015.pdf
https://arxiv.org/abs/1501.03202},
doi = {10.1080/00107514.2015.1063233},
year = {2015},
date = {2015-07-31},
urldate = {2015-01-01},
journal = {Contemporary Physics},
volume = {57},
pages = {60–82},
abstract = {At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, noncommutativity, interference, the no-cloning theorem, and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding – the intrinsically quantum mechanical aspects of Nature. The most famous of these is Bell's theorem, but we also review two more recent results in this area. Firstly, Hardy's theorem shows that even a finite dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey–Barrett–Rudolph theorem shows that the wave-function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, noncommutativity, interference, the no-cloning theorem, and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding – the intrinsically quantum mechanical aspects of Nature. The most famous of these is Bell's theorem, but we also review two more recent results in this area. Firstly, Hardy's theorem shows that even a finite dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey–Barrett–Rudolph theorem shows that the wave-function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems.
2014
Leifer, M. S.; Spekkens, R. W.
A Bayesian approach to compatibility, improvement, and pooling of quantum states Journal Article
In: J. Phys. A, vol. 47, pp. 275301, 2014, (Selected by the editors for inclusion in the "Highlights of 2014" collection.).
@article{Leifer:2014a,
title = {A Bayesian approach to compatibility, improvement, and pooling of quantum states},
author = {M. S. Leifer and R. W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2014a.pdf
https://arxiv.org/abs/1110.1085},
doi = {10.1088/1751-8113/47/27/275301},
year = {2014},
date = {2014-06-18},
urldate = {2014-01-01},
journal = {J. Phys. A},
volume = {47},
pages = {275301},
abstract = {In approaches to quantum theory in which the quantum state is regarded as a representation of knowledge, information, or belief, two agents can assign different states to the same quantum system. This raises two questions: when are such state assignments compatible? And how should the state assignments of different agents be reconciled? In this paper, we address these questions from the perspective of the recently developed conditional states formalism for quantum theory (Leifer M S and Spekkens R W 2013 Phys. Rev. A 88 052310). Specifically, we derive a compatibility criterion proposed by Brun, Finkelstein and Mermin from the requirement that, upon acquiring data, agents should update their states using a quantum generalization of Bayesian conditioning. We provide two alternative arguments for this criterion, based on the objective and subjective Bayesian interpretations of probability theory. We then apply the same methodology to the problem of quantum state improvement, i.e. how to update your state when you learn someone else's state assignment, and to quantum state pooling, i.e. how to combine the state assignments of several agents into a single assignment that accurately represents the views of the group. In particular, we derive a pooling rule previously proposed by Spekkens and Wiseman under much weaker assumptions than those made in the original derivation. All of our results apply to a much broader class of experimental scenarios than have been considered previously in this context.},
note = {Selected by the editors for inclusion in the "Highlights of 2014" collection.},
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pubstate = {published},
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}
In approaches to quantum theory in which the quantum state is regarded as a representation of knowledge, information, or belief, two agents can assign different states to the same quantum system. This raises two questions: when are such state assignments compatible? And how should the state assignments of different agents be reconciled? In this paper, we address these questions from the perspective of the recently developed conditional states formalism for quantum theory (Leifer M S and Spekkens R W 2013 Phys. Rev. A 88 052310). Specifically, we derive a compatibility criterion proposed by Brun, Finkelstein and Mermin from the requirement that, upon acquiring data, agents should update their states using a quantum generalization of Bayesian conditioning. We provide two alternative arguments for this criterion, based on the objective and subjective Bayesian interpretations of probability theory. We then apply the same methodology to the problem of quantum state improvement, i.e. how to update your state when you learn someone else's state assignment, and to quantum state pooling, i.e. how to combine the state assignments of several agents into a single assignment that accurately represents the views of the group. In particular, we derive a pooling rule previously proposed by Spekkens and Wiseman under much weaker assumptions than those made in the original derivation. All of our results apply to a much broader class of experimental scenarios than have been considered previously in this context.
Leifer, M. S.
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states Journal Article
In: Phys. Rev. Lett., vol. 112, pp. 160404, 2014.
@article{Leifer:2014,
title = {Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2014.pdf
https://arxiv.org/abs/1401.7996},
doi = {10.1103/PhysRevLett.112.160404},
year = {2014},
date = {2014-04-25},
urldate = {2014-01-01},
journal = {Phys. Rev. Lett.},
volume = {112},
pages = {160404},
abstract = {The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this letter, I exhibit a family of states for which the ratio of these two quantities must be ( <= 2dexp(-cd)) in Hilbert spaces of dimension (d) that are divisible by (4). This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases.},
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The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this letter, I exhibit a family of states for which the ratio of these two quantities must be ( <= 2dexp(-cd)) in Hilbert spaces of dimension (d) that are divisible by (4). This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases.
Leifer, M. S.
Is the quantum state real? An extended review of psi-ontology theorems Journal Article
In: Quanta, vol. 3, no. 1, pp. 67–155, 2014.
@article{Leifer:2014b,
title = {Is the quantum state real? An extended review of psi-ontology theorems},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2014b.pdf
https://arxiv.org/abs/1409.1570},
doi = {10.12743/quanta.v3i1.22},
year = {2014},
date = {2014-01-01},
urldate = {2014-01-01},
journal = {Quanta},
volume = {3},
number = {1},
pages = {67–155},
abstract = {Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts.},
keywords = {},
pubstate = {published},
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Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts.
2013
Leifer, M. S.; Spekkens, R. W.
Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference Journal Article
In: Phys. Rev. A, vol. 88, no. 5, pp. 052130, 2013.
@article{Leifer:2013,
title = {Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference},
author = {M. S. Leifer and R. W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2013.pdf
https://arxiv.org/abs/1107.5849},
doi = {10.1103/PhysRevA.88.052130},
year = {2013},
date = {2013-11-27},
urldate = {2013-01-01},
journal = {Phys. Rev. A},
volume = {88},
number = {5},
pages = {052130},
abstract = {Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes’ theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.},
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pubstate = {published},
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Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes’ theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.
Leifer, M. S.; Maroney, O. J. E.
Maximally epistemic interpretations of the quantum state and contextuality Journal Article
In: Phys. Rev. Lett., vol. 110, no. 12, pp. 120401, 2013.
@article{Leifer:2012,
title = {Maximally epistemic interpretations of the quantum state and contextuality},
author = {M. S. Leifer and O. J. E. Maroney},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2013.pdf
https://arxiv.org/abs/1208.5132},
doi = {10.1103/PhysRevLett.110.120401},
year = {2013},
date = {2013-03-20},
urldate = {2013-01-01},
journal = {Phys. Rev. Lett.},
volume = {110},
number = {12},
pages = {120401},
abstract = {We examine the relationship between quantum contextuality (in both the standard Kochen-Specker sense and in the generalised sense proposed by Spekkens) and models of quantum theory in which the quantum state is maximally epistemic. We find that preparation noncontextual models must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual. This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models. The implication from preparation noncontextual to maximally epistemic then also yields a proof of Bell's theorem from an EPR-like argument.},
keywords = {},
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We examine the relationship between quantum contextuality (in both the standard Kochen-Specker sense and in the generalised sense proposed by Spekkens) and models of quantum theory in which the quantum state is maximally epistemic. We find that preparation noncontextual models must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual. This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models. The implication from preparation noncontextual to maximally epistemic then also yields a proof of Bell's theorem from an EPR-like argument.
2012
Barnum, H.; Barrett, J.; Clark, L.; Leifer, M.; Spekkens, R.; Stepanik, N.; Wilce, A.; Wilke, R.
Entropy and information causality in general probabilistic theories (addendum) Journal Article
In: New J. Phys., vol. 14, pp. 129401, 2012.
@article{Barnum:2012,
title = {Entropy and information causality in general probabilistic theories (addendum)},
author = {H. Barnum and J. Barrett and L. Clark and M. Leifer and R. Spekkens and N. Stepanik and A. Wilce and R. Wilke},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barnum-2012.pdf},
doi = {10.1088/1367-2630/14/12/129401},
year = {2012},
date = {2012-12-05},
urldate = {2012-01-01},
journal = {New J. Phys.},
volume = {14},
pages = {129401},
abstract = {In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of that paper.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of that paper.
2010
Barnum, H.; Barrett, J.; Clark, L.; Leifer, M.; Spekkens, R.; Stepanik, N.; Wilce, A.; Wilke, R.
Entropy and information causality in general probabilistic theories Journal Article
In: New J. Phys., vol. 12, pp. 033024, 2010.
@article{Barnum:2010,
title = {Entropy and information causality in general probabilistic theories},
author = {H. Barnum and J. Barrett and L. Clark and M. Leifer and R. Spekkens and N. Stepanik and A. Wilce and R. Wilke},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barnum-2010.pdf
https://arxiv.org/abs/0909.5075},
doi = {10.1088/1367-2630/12/3/033024},
year = {2010},
date = {2010-03-01},
urldate = {2010-01-01},
journal = {New J. Phys.},
volume = {12},
pages = {033024},
abstract = {We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)<I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu–Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)<I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu–Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.
2009
Barrett, Jonathan; Leifer, Matthew
The de Finetti theorem for test spaces Journal Article
In: New J. Phys., vol. 11, pp. 033024, 2009.
@article{Barrett:2009,
title = {The de Finetti theorem for test spaces},
author = {Jonathan Barrett and Matthew Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barrett-2009.pdf
https://arxiv.org/abs/0712.2265},
doi = {10.1088/1367-2630/11/3/033024},
year = {2009},
date = {2009-03-01},
urldate = {2009-01-01},
journal = {New J. Phys.},
volume = {11},
pages = {033024},
abstract = {We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
2008
Leifer, Matthew; Poulin, David
Quantum Graphical Models and Belief Propagation Journal Article
In: Ann. Phys., vol. 323, pp. 1899, 2008.
@article{Leifer:2008,
title = {Quantum Graphical Models and Belief Propagation},
author = {Matthew Leifer and David Poulin},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2008.pdf
https://arxiv.org/abs/0708.1337},
doi = {10.1016/j.aop.2007.10.001},
year = {2008},
date = {2008-08-01},
urldate = {2008-01-01},
journal = {Ann. Phys.},
volume = {323},
pages = {1899},
abstract = {Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley–Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley–Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.
2007
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
Generalized no-broadcasting theorem Journal Article
In: Phys. Rev. Lett., vol. 99, pp. 240501, 2007.
@article{Barnum:2007,
title = {Generalized no-broadcasting theorem},
author = {Howard Barnum and Jonathan Barrett and Matthew Leifer and Alexander Wilce},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barnum-2007.pdf
https://arxiv.org/abs/0707.0620},
doi = {10.1103/PhysRevLett.99.240501},
year = {2007},
date = {2007-12-13},
urldate = {2007-01-01},
journal = {Phys. Rev. Lett.},
volume = {99},
pages = {240501},
abstract = {We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``superquantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``superquantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
2006
Leifer, M. S.
Quantum Dynamics as an analog of Conditional Probability Journal Article
In: Phys. Rev. A, vol. 74, pp. 042310, 2006.
@article{Leifer:2006,
title = {Quantum Dynamics as an analog of Conditional Probability},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2006.pdf
https://arxiv.org/abs/quant-ph/0606022},
doi = {10.1103/PhysRevA.74.042310},
year = {2006},
date = {2006-10-12},
urldate = {2006-01-01},
journal = {Phys. Rev. A},
volume = {74},
pages = {042310},
abstract = {Quantum theory can be regarded as a noncommutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. This isomorphism is given an operational interpretation in terms of statistical correlations between ensemble preparation procedures and outcomes of measurements. Finally, the isomorphism is applied to elucidate the connection between no-cloning and no-broadcasting theorems and the monogamy of entanglement, and a simplified proof of the no-broadcasting theorem is obtained as a by-product.},
keywords = {},
pubstate = {published},
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}
Quantum theory can be regarded as a noncommutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. This isomorphism is given an operational interpretation in terms of statistical correlations between ensemble preparation procedures and outcomes of measurements. Finally, the isomorphism is applied to elucidate the connection between no-cloning and no-broadcasting theorems and the monogamy of entanglement, and a simplified proof of the no-broadcasting theorem is obtained as a by-product.
2005
Leifer, M. S.; Spekkens, R. W.
Pre- and Post-Selection paradoxes and contextuality in quantum mechanics Journal Article
In: Phys. Rev. Lett., vol. 95, pp. 200405, 2005.
@article{Leifer:2005,
title = {Pre- and Post-Selection paradoxes and contextuality in quantum mechanics},
author = {M. S. Leifer and R. W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2005.pdf
https://arxiv.org/abs/quant-ph/0412178},
doi = {10.1103/PhysRevLett.95.200405},
year = {2005},
date = {2005-11-11},
urldate = {2005-01-01},
journal = {Phys. Rev. Lett.},
volume = {95},
pages = {200405},
abstract = {Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post-selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of the impossibility of a noncontextual hidden variable theory. This proof is obtained by considering all the measurements involved in the paradoxical effect—the preselection, the post-selection, and the alternative possible intermediate measurements—as alternative possible measurements at a single time.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post-selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of the impossibility of a noncontextual hidden variable theory. This proof is obtained by considering all the measurements involved in the paradoxical effect—the preselection, the post-selection, and the alternative possible intermediate measurements—as alternative possible measurements at a single time.
Barrett, Jonathan; Leifer, Matthew; Tumulka, Roderich
Bell's Jump Process in Discrete Time Journal Article
In: Europhysics Letters, vol. 72, no. 5, pp. 685-690, 2005.
@article{Barrett:2005,
title = {Bell's Jump Process in Discrete Time},
author = {Jonathan Barrett and Matthew Leifer and Roderich Tumulka},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barrett-2005.pdf
https://arxiv.org/abs/quant-ph/0506066},
doi = {10.1209/epl/i2005-10297-5},
year = {2005},
date = {2005-10-28},
urldate = {2005-01-01},
journal = {Europhysics Letters},
volume = {72},
number = {5},
pages = {685-690},
abstract = {The jump process introduced by J. S. Bell in 1986, for defining a quantum field theory without observers, presupposes that space is discrete whereas time is continuous. In this letter, our interest is to find an analogous process in discrete time. We argue that a genuine analog does not exist, but provide examples of processes in discrete time that could be used as a replacement.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The jump process introduced by J. S. Bell in 1986, for defining a quantum field theory without observers, presupposes that space is discrete whereas time is continuous. In this letter, our interest is to find an analogous process in discrete time. We argue that a genuine analog does not exist, but provide examples of processes in discrete time that could be used as a replacement.
2004
Leifer, M. S.; Linden, N.; Winter, A.
Measuring Polynomial Invariants of Multi-Party Quantum States Journal Article
In: Phys. Rev. A, vol. 69, pp. 052304, 2004.
@article{Leifer:2004,
title = {Measuring Polynomial Invariants of Multi-Party Quantum States},
author = {M. S. Leifer and N. Linden and A. Winter},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2004.pdf
https://arxiv.org/abs/quant-ph/0308008},
doi = {10.1103/PhysRevA.69.052304},
year = {2004},
date = {2004-05-07},
urldate = {2004-01-01},
journal = {Phys. Rev. A},
volume = {69},
pages = {052304},
abstract = {We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.
2003
Leifer, M. S.; Henderson, L.; Linden, N.
Optimal Entanglement Generation from Quantum Operations Journal Article
In: Phys. Rev. A, vol. 67, pp. 012306, 2003.
@article{Leifer:2003,
title = {Optimal Entanglement Generation from Quantum Operations},
author = {M. S. Leifer and L. Henderson and N. Linden},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2003.pdf
https://arxiv.org/abs/quant-ph/0205055},
doi = {10.1103/PhysRevA.67.012306},
year = {2003},
date = {2003-01-13},
urldate = {2003-01-01},
journal = {Phys. Rev. A},
volume = {67},
pages = {012306},
abstract = {We consider how much entanglement can be produced by a nonlocal two-qubit unitary operation, UAB—the entangling capacity of UAB. For a single application of UAB, with no ancillas, we find the entangling capacity and show that it generally helps to act with UAB on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider how much entanglement can be produced by a nonlocal two-qubit unitary operation, UAB—the entangling capacity of UAB. For a single application of UAB, with no ancillas, we find the entangling capacity and show that it generally helps to act with UAB on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.
2002
Bennett, C. H.; Cirac, J. I.; Leifer, M. S.; Leung, D. W.; Linden, N.; Popescu, S.; Vidal, G.
Optimal simulation of two-qubit Hamiltonians using general local operations Journal Article
In: Phys. Rev. A, vol. 66, pp. 012305, 2002.
@article{Bennett:2002,
title = {Optimal simulation of two-qubit Hamiltonians using general local operations},
author = {C. H. Bennett and J. I. Cirac and M. S. Leifer and D. W. Leung and N. Linden and S. Popescu and G. Vidal},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/bennett-2002.pdf
https://arxiv.org/abs/quant-ph/0107035},
doi = {10.1103/PhysRevA.66.012305},
year = {2002},
date = {2002-07-19},
urldate = {2002-01-01},
journal = {Phys. Rev. A},
volume = {66},
pages = {012305},
abstract = {We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian HHA+HB. We consider the achievable space of Hamiltonians H such that the evolution e-iHt can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H, there exists a scale factor s such that for all times t the evolution e-iHst can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H, we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian HHA+HB. We consider the achievable space of Hamiltonians H such that the evolution e-iHt can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H, there exists a scale factor s such that for all times t the evolution e-iHst can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H, we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.
Articles in Conference Proceedings
2015
Pusey, Matthew F.; Leifer, Matthew S.
Logical pre- and post-selection paradoxes are proofs of contextuality Proceedings Article
In: Heunen, C.; Selinger, P.; Vicary, J. (Ed.): Proceedings 12th International Workshop on Quantum Physics and Logic, pp. 295–306, 2015.
@inproceedings{Pusey:2015,
title = {Logical pre- and post-selection paradoxes are proofs of contextuality},
author = {Matthew F. Pusey and Matthew S. Leifer},
editor = {C. Heunen and P. Selinger and J. Vicary},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2015.pdf
http://arxiv.org/html/1511.01181v1},
doi = {10.4204/EPTCS.195.22},
year = {2015},
date = {2015-01-01},
urldate = {2015-01-01},
booktitle = {Proceedings 12th International Workshop on Quantum Physics and Logic},
volume = {195},
pages = {295–306},
series = {Electronic Proceedings in Theoretical Computer Science},
abstract = {If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurements with LĂĽders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without LĂĽders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurements with LĂĽders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without LĂĽders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.
2012
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
Teleportation in General Probabilistic Theories Proceedings Article
In: Abramsky, S.; Mislove, M. (Ed.): Mathematical Foundations of Information Flow (Proceedings of the Clifford Lectures 2008), pp. 25–47, American Mathematical Society, 2012.
@inproceedings{Barnum:2012a,
title = {Teleportation in General Probabilistic Theories},
author = {Howard Barnum and Jonathan Barrett and Matthew Leifer and Alexander Wilce},
editor = {S. Abramsky and M. Mislove},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/barnum-2012a.pdf
https://arxiv.org/abs/0805.3553},
doi = {http://dx.doi.org/10.1090/psapm/071/600},
year = {2012},
date = {2012-01-01},
urldate = {2012-01-01},
booktitle = {Mathematical Foundations of Information Flow (Proceedings of the Clifford Lectures 2008)},
volume = {71},
pages = {25–47},
publisher = {American Mathematical Society},
series = {Proceedings of Symposia in Applied Mathematics},
abstract = {In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, em do support a teleportation protocol. We isolate a natural class of composite systems that we term em regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields a large supply of theories, neither classical nor quantum, that support such a protocol.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, em do support a teleportation protocol. We isolate a natural class of composite systems that we term em regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields a large supply of theories, neither classical nor quantum, that support such a protocol.
2008
Barnum, Howard; Dahlsten, Oscar C. O.; Leifer, Matthew; Toner, Ben
Nonclassicality without entanglement enables bit commitment Proceedings Article
In: Proceedings of IEEE Information Theory Workshop, 2008, pp. 386-390, 2008.
@inproceedings{Barnum:2008,
title = {Nonclassicality without entanglement enables bit commitment},
author = {Howard Barnum and Oscar C. O. Dahlsten and Matthew Leifer and Ben Toner},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/barnum-2008.pdf
https://arxiv.org/abs/0803.1264},
doi = {10.1109/ITW.2008.4578692},
year = {2008},
date = {2008-07-25},
urldate = {2008-01-01},
booktitle = {Proceedings of IEEE Information Theory Workshop, 2008},
pages = {386-390},
abstract = {We investigate the existence of secure bit commitment protocols in the convex framework for probabilistic theories. The theory makes only minimal assumptions, and can be used to formalize quantum theory, classical probability theory, and a host of other possibilities. We prove that in all such theories that are locally non-classical but do not have entanglement, there exists a bit commitment protocol that is exponentially secure in the number of systems used.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
We investigate the existence of secure bit commitment protocols in the convex framework for probabilistic theories. The theory makes only minimal assumptions, and can be used to formalize quantum theory, classical probability theory, and a host of other possibilities. We prove that in all such theories that are locally non-classical but do not have entanglement, there exists a bit commitment protocol that is exponentially secure in the number of systems used.
2007
Leifer, M. S.
Conditional Density Operators and the Subjectivity of Quantum Operations Proceedings Article
In: Adenier, G.; Fuchs, C. A.; Khrennikov, A. Yu. (Ed.): Foundations of Probability and Physics-4, pp. 172-186, AIP, 2007.
@inproceedings{Leifer:2007,
title = {Conditional Density Operators and the Subjectivity of Quantum Operations},
author = {M. S. Leifer},
editor = {G. Adenier and C. A. Fuchs and A. Yu. Khrennikov},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2007.pdf
https://arxiv.org/abs/quant-ph/0611233},
doi = {10.1063/1.2713456},
year = {2007},
date = {2007-02-21},
urldate = {2007-02-21},
booktitle = {Foundations of Probability and Physics-4},
volume = {889},
pages = {172-186},
publisher = {AIP},
series = {AIP Conference Proceedings},
abstract = {Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is addressed. In particular, we ask this of the dynamical aspects of the formalism, such as Hamiltonians and unitary operators. Whilst some operations, such as the update maps corresponding to a complete projective measurement, must be subjective, the situation is not so clear in other cases. Here, it is argued that all trace preserving completely positive maps, including unitary operators, should be regarded as subjective, in the same sense as a classical conditional probability distribution. The argument is based on a reworking of the Choi-Jamiolkowski isomorphism in terms of ``conditional'' density operators and trace preserving completely positive maps, which mimics the relationship between conditional probabilities and stochastic maps in classical probability.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is addressed. In particular, we ask this of the dynamical aspects of the formalism, such as Hamiltonians and unitary operators. Whilst some operations, such as the update maps corresponding to a complete projective measurement, must be subjective, the situation is not so clear in other cases. Here, it is argued that all trace preserving completely positive maps, including unitary operators, should be regarded as subjective, in the same sense as a classical conditional probability distribution. The argument is based on a reworking of the Choi-Jamiolkowski isomorphism in terms of ``conditional'' density operators and trace preserving completely positive maps, which mimics the relationship between conditional probabilities and stochastic maps in classical probability.
2005
Leifer, M. S.; Spekkens, R. W.
Logical Pre- and Post-Selection paradoxes, measurement-disturbance and contextuality Proceedings Article
In: Proceedings of Quantum Structures 2004, pp. 1977-1987, Springer Netherlands, 2005.
@inproceedings{Leifer:2005a,
title = {Logical Pre- and Post-Selection paradoxes, measurement-disturbance and contextuality},
author = {M. S. Leifer and R. W. Spekkens},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leifer-2005a.pdf
https://arxiv.org/abs/quant-ph/0412179},
doi = {10.1007/s10773-005-8975-1},
year = {2005},
date = {2005-11-01},
urldate = {2005-01-01},
booktitle = {Proceedings of Quantum Structures 2004},
journal = {Int. J. Theor. Phys.},
volume = {44},
number = {11},
pages = {1977-1987},
publisher = {Springer Netherlands},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Book Chapters
2021
Leifer, Matthew
Quantum entanglement Book Section
In: World Book Encyclopedia, 2021.
@incollection{Leifer2021,
title = {Quantum entanglement},
author = {Matthew Leifer},
url = {https://worldbookonline.com/student-new/#/article/home/757992},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
booktitle = {World Book Encyclopedia},
edition = {2021 Edition},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
2019
Leifer, Matthew
Against Fundamentalism Book Section
In: Aguirre, A.; Foster, B.; Merali, Z. (Ed.): What is Fundamental?, pp. 13-25, Springer, 2019, (Second Prize winner in 2017 FQXi Essay Contest).
@incollection{Leifer2019,
title = {Against Fundamentalism},
author = {Matthew Leifer},
editor = {A. Aguirre and B. Foster and Z. Merali},
url = {https://arxiv.org/abs/1810.05272https://mattleifer.info/wordpress/wp-content/uploads/2024/08/BookChapters2019Leifer.pdf},
doi = {10.1007/978-3-030-11301-8_3},
year = {2019},
date = {2019-03-22},
urldate = {2019-03-22},
booktitle = {What is Fundamental?},
pages = {13-25},
publisher = {Springer},
series = {The Frontiers Collection},
abstract = {In this essay, I argue that the idea that there is a most fundamental discipline, or level of reality, is mistaken. My argument is a result of my experiences with the “science wars”, a debate that raged between scientists and sociologists in the 1990s over whether science can lay claim to objective truth. These debates shook my faith in physicalism, i.e. the idea that everything boils down to physics. I outline a theory of knowledge that I first proposed in my 2015 FQXi essay on which knowledge has the structure of a scale-free network. In this theory, although some disciplines are in a sense “more fundamental” than others, we never get to a “most fundamental” discipline. Instead, we get hubs of knowledge that have equal importance. This structure can explain why many physicists believe that physics is fundamental, while some sociologists believe that sociology is fundamental. This updated version of the essay includes an appendix with my responses to the discussion of this essay on the FQXi website.},
note = {Second Prize winner in 2017 FQXi Essay Contest},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
In this essay, I argue that the idea that there is a most fundamental discipline, or level of reality, is mistaken. My argument is a result of my experiences with the “science wars”, a debate that raged between scientists and sociologists in the 1990s over whether science can lay claim to objective truth. These debates shook my faith in physicalism, i.e. the idea that everything boils down to physics. I outline a theory of knowledge that I first proposed in my 2015 FQXi essay on which knowledge has the structure of a scale-free network. In this theory, although some disciplines are in a sense “more fundamental” than others, we never get to a “most fundamental” discipline. Instead, we get hubs of knowledge that have equal importance. This structure can explain why many physicists believe that physics is fundamental, while some sociologists believe that sociology is fundamental. This updated version of the essay includes an appendix with my responses to the discussion of this essay on the FQXi website.
2016
Leifer, M. S.
Mathematics is Physics Book Section
In: Aguirre, A.; Foster, B.; Merali, Z. (Ed.): Trick or Truth? The Mysterious Connection Between Physics and Mathematics, pp. 21–40, Springer, 2016, (Second prize winner of the 2015 FQXi essay contest.).
@incollection{Leifer2016,
title = {Mathematics is Physics},
author = {M. S. Leifer},
editor = {A. Aguirre and B. Foster and Z. Merali},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/BookChapters2016Leifer.pdf
https://forums.fqxi.org/d/2364-mathematics-is-physics-by-matthew-saul-leifer
https://arxiv.org/abs/1508.02770
},
doi = {10.1007/978-3-319-27495-9_3},
year = {2016},
date = {2016-02-21},
urldate = {2016-01-01},
booktitle = {Trick or Truth? The Mysterious Connection Between Physics and Mathematics},
pages = {21–40},
publisher = {Springer},
abstract = {In this essay, I argue that mathematics is a natural science—just like physics, chemistry, or biology—and that this can explain the alleged “unreasonable” effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers’ essay [1] and comments that were made on the FQXi website [2].},
note = {Second prize winner of the 2015 FQXi essay contest.},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
In this essay, I argue that mathematics is a natural science—just like physics, chemistry, or biology—and that this can explain the alleged “unreasonable” effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics. This version of the essay contains an addendum responding to Slyvia Wenmackers’ essay [1] and comments that were made on the FQXi website [2].
2015
Leifer, M. S.
"It from bit'' and the Quantum Probability Rule Book Section
In: Aguirre, A.; Foster, B.; Merali, Z. (Ed.): It From Bit or Bit From It? On Physics and Information, pp. 5–23, Springer, 2015, (Winning entry of the 2013 FQXi essay contest.).
@incollection{Leifer2015,
title = {"It from bit'' and the Quantum Probability Rule},
author = {M. S. Leifer},
editor = {A. Aguirre and B. Foster and Z. Merali},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leiferfqxi2013.pdf
https://forums.fqxi.org/d/1821-it-from-bit-and-the-quantum-probability-rule-by-matthew-saul-leifer
https://arxiv.org/abs/1311.0857},
doi = {10.1007/978-3-319-12946-4_2},
year = {2015},
date = {2015-02-04},
urldate = {2015-01-01},
booktitle = {It From Bit or Bit From It? On Physics and Information},
pages = {5–23},
publisher = {Springer},
abstract = {I argue that, on the subjective Bayesian interpretation of probability, “it from bit” requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or “bit from it”. I then explain why this does not conflict with “it from bit”. This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.},
note = {Winning entry of the 2013 FQXi essay contest.},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
I argue that, on the subjective Bayesian interpretation of probability, “it from bit” requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or “bit from it”. I then explain why this does not conflict with “it from bit”. This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.
Preprints
2023
Schmid, David; Yīng, Yìlè; Leifer, Matthew
A review and analysis of six extended Wigner's friend arguments Unpublished
2023.
@unpublished{Schmid2023,
title = {A review and analysis of six extended Wigner's friend arguments},
author = {David Schmid and Yìlè Yīng and Matthew Leifer},
url = {https://arxiv.org/abs/2308.16220},
doi = {10.48550/arXiv.2308.16220},
year = {2023},
date = {2023-10-10},
abstract = {The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of quantum theory, most modern interpretations have no trouble in resolving the difficulty. Recently, a number of extensions of Wigner's ideas have been proposed. We provide a gentle introduction to six such arguments, modifying the specifics of many of them so that they are as simple and unified as possible. In particular, we show that all of the arguments hinge on assumptions about correlations between measurement outcomes that are not accessible to any observer, even in principle. We then provide a critical analysis of each argument, focusing especially on how well one can motivate the required assumptions regarding these inaccessible correlations. Although we argue that some of these assumptions are not entirely well-motivated, all of the arguments do shed light on the nature of quantum theory, especially when concerning the description of agents and their measurements. Although there are other possible responses, the most compelling of these no-go theorems can be taken to support the view that measurement outcomes are perspectival rather than absolute.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of quantum theory, most modern interpretations have no trouble in resolving the difficulty. Recently, a number of extensions of Wigner's ideas have been proposed. We provide a gentle introduction to six such arguments, modifying the specifics of many of them so that they are as simple and unified as possible. In particular, we show that all of the arguments hinge on assumptions about correlations between measurement outcomes that are not accessible to any observer, even in principle. We then provide a critical analysis of each argument, focusing especially on how well one can motivate the required assumptions regarding these inaccessible correlations. Although we argue that some of these assumptions are not entirely well-motivated, all of the arguments do shed light on the nature of quantum theory, especially when concerning the description of agents and their measurements. Although there are other possible responses, the most compelling of these no-go theorems can be taken to support the view that measurement outcomes are perspectival rather than absolute.
2022
Catani, Lorenzo; Leifer, Matthew; Schmid, David; Spekkens, Robert W.
Reply to "Comment on 'Why interference phenomena do not capture the essence of quantum theory' " Unpublished
2022.
@unpublished{Catani2022b,
title = {Reply to "Comment on 'Why interference phenomena do not capture the essence of quantum theory' "},
author = {Lorenzo Catani and Matthew Leifer and David Schmid and Robert W. Spekkens},
url = {https://arxiv.org/abs/2207.11791},
doi = {10.48550/arXiv.2207.11791},
year = {2022},
date = {2022-07-24},
abstract = {Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.
Leifer, Matthew; Duarte, Cristhiano
Generalizing Aumann's Agreement Theorem Unpublished
2022.
@unpublished{Leifer2022,
title = {Generalizing Aumann's Agreement Theorem},
author = {Matthew Leifer and Cristhiano Duarte},
url = {https://arxiv.org/abs/2202.02156},
doi = {10.48550/arXiv.2202.02156},
year = {2022},
date = {2022-02-04},
abstract = {Aumann's celebrated theorem says that a group of agents who once shared a common prior probability distribution cannot assign different posteriors to a given proposition, should these agents have common knowledge about their posteriors. In other words, rational agents cannot agree to disagree. Aumann's agreement theorem was one of the first attempts to formalise and explore the role played by common knowledge in decision theory. Recently, we have seen a resurfacing of the debate around possible (quantum) extensions of Aumann's results. This paper contributes to this discussion. First, as expected, we argue that agreeing to disagree is impossible in quantum theory. Secondly, and based on the quantum argument, we show that agreeing to disagree is also forbidden in any generalised probability theory.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
Aumann's celebrated theorem says that a group of agents who once shared a common prior probability distribution cannot assign different posteriors to a given proposition, should these agents have common knowledge about their posteriors. In other words, rational agents cannot agree to disagree. Aumann's agreement theorem was one of the first attempts to formalise and explore the role played by common knowledge in decision theory. Recently, we have seen a resurfacing of the debate around possible (quantum) extensions of Aumann's results. This paper contributes to this discussion. First, as expected, we argue that agreeing to disagree is impossible in quantum theory. Secondly, and based on the quantum argument, we show that agreeing to disagree is also forbidden in any generalised probability theory.
2020
Duarte, Cristhiano; Amaral, Barbara; Cunha, Marcelo Terra; Leifer, Matthew
Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives Unpublished
2020.
@unpublished{Duarte2020,
title = {Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives},
author = {Cristhiano Duarte and Barbara Amaral and Marcelo Terra Cunha and Matthew Leifer},
url = {https://arxiv.org/abs/2011.10349},
doi = {https://doi.org/10.48550/arXiv.2011.10349},
year = {2020},
date = {2020-11-20},
abstract = {With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the complexity of such description tends to increase with the number of particles. It is thus crucial to build effective quantum theories aiming to understand how the description in one scale emerges from the description of a deeper scale. This contribution explores different mathematical tools to the study of emergent effective dynamics in scenarios where a system is subject to a unitary evolution and the coarse-grained description of it is given by a CPTP map taking the original system into an emph{effective} Hilbert space of smaller dimension. We see that a well-defined effective dynamics can only be defined when some sort of matching between the underlying unitary and the coarse-graining map is satisfied. Our main goal is to use these different tools to derive necessary and sufficient conditions for this matching in the general case.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the complexity of such description tends to increase with the number of particles. It is thus crucial to build effective quantum theories aiming to understand how the description in one scale emerges from the description of a deeper scale. This contribution explores different mathematical tools to the study of emergent effective dynamics in scenarios where a system is subject to a unitary evolution and the coarse-grained description of it is given by a CPTP map taking the original system into an emph{effective} Hilbert space of smaller dimension. We see that a well-defined effective dynamics can only be defined when some sort of matching between the underlying unitary and the coarse-graining map is satisfied. Our main goal is to use these different tools to derive necessary and sufficient conditions for this matching in the general case.
2017
Leifer, Matthew S.
Time Symmetric Quantum Theory Without Retrocausality? A Reply to Tim Maudlin Unpublished
2017.
@unpublished{Leifer2017,
title = {Time Symmetric Quantum Theory Without Retrocausality? A Reply to Tim Maudlin},
author = {Matthew S. Leifer},
url = {https://arxiv.org/abs/1708.04364},
doi = {10.48550/arXiv.1708.04364},
year = {2017},
date = {2017-08-15},
abstract = {In arXiv:1707.08641, Tim Maudlin claims to construct a counterexample to the result of Proc. Roy. Soc. A vol. 473, iss. 2202, 2017 (arXiv:1607.07871), in which it was shown that no realist model satisfying a certain notion of time-symmetry (in addition to three other assumptions) can reproduce the predictions of quantum theory without retrocausality (influences travelling backwards in time). In this comment, I explain why Maudlin's model is not a counterexample because it does not satisfy our time-symmetry assumption. I also explain why Maudlin's claim that one of the Lemmas we used in our proof is incorrect is wrong.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
In arXiv:1707.08641, Tim Maudlin claims to construct a counterexample to the result of Proc. Roy. Soc. A vol. 473, iss. 2202, 2017 (arXiv:1607.07871), in which it was shown that no realist model satisfying a certain notion of time-symmetry (in addition to three other assumptions) can reproduce the predictions of quantum theory without retrocausality (influences travelling backwards in time). In this comment, I explain why Maudlin's model is not a counterexample because it does not satisfy our time-symmetry assumption. I also explain why Maudlin's claim that one of the Lemmas we used in our proof is incorrect is wrong.
2015
Fritz, Tobias; Leifer, Matthew
Plausibility measures on test spaces Unpublished
2015.
@unpublished{Fritz2015,
title = {Plausibility measures on test spaces},
author = {Tobias Fritz and Matthew Leifer},
url = {https://arxiv.org/abs/1505.01151},
year = {2015},
date = {2015-05-05},
urldate = {2015-01-01},
abstract = {Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of plausibility measures has only been developed for classical sample spaces. In this paper, we generalize the theory to test spaces, so that they can be applied to general operational theories, and to quantum theory in particular. Our main results are two theorems on when a plausibility measure agrees with a probability measure, i.e. when its comparative relations coincide with those of a probability measure. For strictly finite test spaces we obtain a precise analogue of the classical result that the Archimedean condition is necessary and sufficient for agreement between a plausibility and a probability measure. In the locally finite case, we prove a slightly weaker result that the Archimedean condition implies almost agreement.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of plausibility measures has only been developed for classical sample spaces. In this paper, we generalize the theory to test spaces, so that they can be applied to general operational theories, and to quantum theory in particular. Our main results are two theorems on when a plausibility measure agrees with a probability measure, i.e. when its comparative relations coincide with those of a probability measure. For strictly finite test spaces we obtain a precise analogue of the classical result that the Archimedean condition is necessary and sufficient for agreement between a plausibility and a probability measure. In the locally finite case, we prove a slightly weaker result that the Archimedean condition implies almost agreement.
2006
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
Cloning and Broadcasting in Generic Probabilistic Theories Unpublished
2006.
@unpublished{Barnum:2006,
title = {Cloning and Broadcasting in Generic Probabilistic Theories},
author = {Howard Barnum and Jonathan Barrett and Matthew Leifer and Alexander Wilce},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/barnum-2006.pdf
https://arxiv.org/abs/quant-ph/0611295},
doi = {10.48550/arXiv.quant-ph/0611295},
year = {2006},
date = {2006-01-01},
urldate = {2006-01-01},
abstract = {We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially em any non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially em any non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.
2005
Leifer, M. S.
Nondeterministic testing of Sequential Quantum Logic propositions on a quantum computer Unpublished
2005.
@unpublished{Leifer:2005b,
title = {Nondeterministic testing of Sequential Quantum Logic propositions on a quantum computer},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/leifer-2005b.pdf
https://arxiv.org/abs/quant-ph/0509193},
doi = {10.48550/arXiv.quant-ph/0509193},
year = {2005},
date = {2005-09-28},
urldate = {2005-01-01},
abstract = {In the past few years it has been shown that universal quantum computation can be obtained by projective measurements alone, with no need for unitary gates. This suggests that the underlying logic of quantum computing may be an algebra of sequences of quantum measurements rather than an algebra of products of unitary operators. Such a Sequential Quantum Logic (SQL) was developed in the late 70's and has more recently been applied to the consistent histories framework of quantum mechanics as a possible route to the theory of quantum gravity. In this letter, I give a method for deciding the truth of a proposition in SQL with nonzero probability of success on a quantum computer.},
keywords = {},
pubstate = {published},
tppubtype = {unpublished}
}
In the past few years it has been shown that universal quantum computation can be obtained by projective measurements alone, with no need for unitary gates. This suggests that the underlying logic of quantum computing may be an algebra of sequences of quantum measurements rather than an algebra of products of unitary operators. Such a Sequential Quantum Logic (SQL) was developed in the late 70's and has more recently been applied to the consistent histories framework of quantum mechanics as a possible route to the theory of quantum gravity. In this letter, I give a method for deciding the truth of a proposition in SQL with nonzero probability of success on a quantum computer.
Book Reviews
2019
Leifer, Matthew
Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime by Sean Carroll Journal Article
In: Physics Today, vol. 72, iss. 12, pp. 56-57, 2019.
@article{Leifer2019b,
title = {Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime by Sean Carroll},
author = {Matthew Leifer},
url = {https://pubs.aip.org/physicstoday/article/72/12/56/811728/Does-the-many-worlds-interpretation-hold-the-key},
doi = {10.1063/PT.3.4366},
year = {2019},
date = {2019-12-01},
journal = {Physics Today},
volume = {72},
issue = {12},
pages = {56-57},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2017
Leifer, Matthew
QBism: The Future of Quantum Physics by Hans Christian von Baeyer Journal Article
In: Physics in Perspective, vol. 19, pp. 17-83, 2017.
@article{Leifer2017b,
title = {QBism: The Future of Quantum Physics by Hans Christian von Baeyer},
author = {Matthew Leifer},
url = {https://digitalcommons.chapman.edu/scs_articles/561/},
doi = {10.1007/s00016-017-0196-5},
year = {2017},
date = {2017-03-22},
journal = {Physics in Perspective},
volume = {19},
pages = {17-83},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2016
Leifer, M. S.
Einstein and the Quantum: The Quest of the Valiant Swabian by A. Douglas Stone Journal Article
In: Spontaneous Generations, vol. 8, no. 1, pp. 105–108, 2016.
@article{LeiferStone,
title = {Einstein and the Quantum: The Quest of the Valiant Swabian by A. Douglas Stone},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/leiferstone.pdf
https://spontaneousgenerations.library.utoronto.ca/index.php/SpontaneousGenerations/article/view/20940},
year = {2016},
date = {2016-06-17},
urldate = {2016-06-17},
journal = {Spontaneous Generations},
volume = {8},
number = {1},
pages = {105–108},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2013
Leifer, M. S.
In: The Quantum Times (Newsletter of the APS Topical Group on Quantum Information), vol. 7, no. 2, pp. 8–10, 2013.
@article{LeiferGribbinDowling,
title = {Computing With Quantum Cats: From Colossus To Qubits by John Gribbin and Schrödinger's Killer App: Race To Build The World's First Quantum Computer by Jonathan Dowling},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/QuantumTimesvol7num2.pdf
https://higherlogicdownload.s3.amazonaws.com/APS/0f1934e0-5e10-4541-a71b-2297f1958ea3/UploadedImages/Documents/vol7num2.pdf},
year = {2013},
date = {2013-07-01},
urldate = {2013-01-01},
journal = {The Quantum Times (Newsletter of the APS Topical Group on Quantum Information)},
volume = {7},
number = {2},
pages = {8–10},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2012
Leifer, M. S.
The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement by Teiko Heinosaari and Mario Ziman Journal Article
In: The Quantum Times (Newsletter of the APS Topical Group on Quantum Information), vol. 7, no. 1, pp. 11–13, 2012.
@article{LeiferHeinosaariZiman,
title = {The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement by Teiko Heinosaari and Mario Ziman},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/QuantumTimesVol7Num1.pdf
https://higherlogicdownload.s3.amazonaws.com/APS/0f1934e0-5e10-4541-a71b-2297f1958ea3/UploadedImages/Documents/vol7num1.pdf},
year = {2012},
date = {2012-06-01},
urldate = {2012-01-01},
journal = {The Quantum Times (Newsletter of the APS Topical Group on Quantum Information)},
volume = {7},
number = {1},
pages = {11–13},
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}
Leifer, M. S.
Elegance and Enigma: The Quantum Interviews by Maximilian Schlosshauer Journal Article
In: American Journal of Physics, vol. 80, no. 3, pp. 266, 2012.
@article{LeiferSchlosshauer,
title = {Elegance and Enigma: The Quantum Interviews by Maximilian Schlosshauer},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2008/10/AJP_Review_Elegance.pdf},
doi = {10.1119/1.3663268},
year = {2012},
date = {2012-03-01},
urldate = {2012-01-01},
journal = {American Journal of Physics},
volume = {80},
number = {3},
pages = {266},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Newsletter Articles
2017
Leifer, Matthew
Gamifying Quantum Theory Journal Article
In: The Quantum Times (Newsletter of the APS Division of Quantum Information), 2017.
@article{Leifer2017c,
title = {Gamifying Quantum Theory},
author = {Matthew Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/NewsletterArticles2017Leifer.pdf},
year = {2017},
date = {2017-03-15},
journal = {The Quantum Times (Newsletter of the APS Division of Quantum Information)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2013
Leifer, M. S.
Point–Counterpoint: Can anything be learned from surveys on the interpretations of quantum mechanics? Journal Article
In: The Quantum Times (Newsletter of the APS Topical Group on Quantum Information), vol. 7, no. 2, pp. 4–6, 2013.
@article{LeiferQT2013,
title = {Point–Counterpoint: Can anything be learned from surveys on the interpretations of quantum mechanics?},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/06/QuantumTimesvol7num2.pdf
https://higherlogicdownload.s3.amazonaws.com/APS/0f1934e0-5e10-4541-a71b-2297f1958ea3/UploadedImages/Documents/vol7num2.pdf},
year = {2013},
date = {2013-07-01},
urldate = {2013-01-01},
journal = {The Quantum Times (Newsletter of the APS Topical Group on Quantum Information)},
volume = {7},
number = {2},
pages = {4–6},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2012
Leifer, M. S.
Response to Griffiths Journal Article
In: The Quantum Times (Newsletter of the APS Topical Group on Quantum Information), vol. 6, no. 4, pp. 6, 2012.
@article{LeiferQT2012,
title = {Response to Griffiths},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/QuantumTimesVol6Num4.pdf
https://higherlogicdownload.s3.amazonaws.com/APS/0f1934e0-5e10-4541-a71b-2297f1958ea3/UploadedImages/Documents/vol6num4.pdf},
year = {2012},
date = {2012-03-01},
urldate = {2012-01-01},
journal = {The Quantum Times (Newsletter of the APS Topical Group on Quantum Information)},
volume = {6},
number = {4},
pages = {6},
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pubstate = {published},
tppubtype = {article}
}
2011
Leifer, M. S.
PBR, EPR, and all that jazz Journal Article
In: The Quantum Times (Newsletter of the APS Topical Group on Quantum Information), vol. 6, no. 3, pp. 1–3, 2011.
@article{LeiferQT2011,
title = {PBR, EPR, and all that jazz},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2024/08/QuantumTimesVol6Num3.pdf
https://higherlogicdownload.s3.amazonaws.com/APS/0f1934e0-5e10-4541-a71b-2297f1958ea3/UploadedImages/Documents/vol6num3.pdf},
year = {2011},
date = {2011-10-01},
urldate = {2011-01-01},
journal = {The Quantum Times (Newsletter of the APS Topical Group on Quantum Information)},
volume = {6},
number = {3},
pages = {1–3},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Ph.D. Thesis
2003
Leifer, M. S.
Entangled Quantum Dynamics PhD Thesis
University of Bristol, 2003.
@phdthesis{LeiferPhd:2003,
title = {Entangled Quantum Dynamics},
author = {M. S. Leifer},
url = {https://mattleifer.info/wordpress/wp-content/uploads/2008/11/mleiferthesis.pdf},
year = {2003},
date = {2003-10-01},
urldate = {2003-10-01},
school = {University of Bristol},
keywords = {},
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tppubtype = {phdthesis}
}