Tag Archives: quantum

The Church of the Smaller Hilbert Space

This is supposed to be a balanced blog, but my nonexistent readership may wish to know exactly what I do believe about quantum mechanics. The document below explains everything.

WARNING: The document below contains geek humor that also parodies the style of a certain well-known religious text. If you don't find jokes about density operators funny and/or you are a devout religious person then you may find its contents offensive. The document below does not necessarily represent the opinions of its author, or indeed any person, animal, alien or sentient artificial intelligence, living, dead or yet to be born.

Ten Commandments of the Church of the Smaller Hilbert Space
Update:  The link is now working.  Apologies for the delay.

The Free Will Theorem

Michael Nielsen recently posted a comment by John Sidles about a preprint by Kochen and Conway that was posted on the quant-ph arXiv yesterday. It's called "The Free Will Theorem", which is certainly a provocative title. Here's my comment on the paper that I left on Mike's blog.

Hmm… I had a look at this paper. The title sounds a bit crackpot, but given the status of the authors I was willing to give it a chance.

First of all the name “Free Will Theorem” opens a whole can of worms, which we probably don’t want to get into. Suffice to say, what they actually prove is an “indeterminism theorem”, i.e. they use a Bell-type argument + a no-signalling requirement to prove that nature must be indeterministic. I have heard similar arguments before, in particular Y. Aharonov and D. Rohlich mention it in their book, although I’ve never seen it written down formally before.

To call this a “free will theorem” one has to get into the debates about whether free will is compatible with determinism and, if not, whether indeterminism even solves the problem. Most contemporary philosophers seem to answer yes and no respectively, so I don’t think this theorem has much to do with free will, although it would take a lot more space to go through the arguments for and against thoroughly.

However, what I did think was interesting about the paper was the “hexagon universe” toy-model that they introduced in the second half of the paper. Given the current interest in understanding aspects of QM via simpler toy theories, e.g. nonlocal boxes and Spekkens toy theory, this might be a useful addition to the canon. I haven’t managed to decipher all the details of this model yet, so I’ll have to defer judgement on that.

Foundations Spring/Summer 2006

Here’s my list of the highlights of the conference season for foundations this year:

  • Foundations of Quantum Information and Entanglement.
  • April 28th-30th: New Directions in the Foundations of Physics – University of Maryland.
    • This is annual meeting is usually interesting. Unfortunately, attendance is by invitation only.
  • May 29th-June 2nd: Beyond the Quantum – Lorentz Centre.
  • June 4th-9th: Foundations of Probability and Physics 4 – Vaxjo.
  • July 9th-14th: Quantum Structures 2006 – Malta.
    • The big “quantum logicy” meeting.
  • 28th November – 3rd December: Quantum Communication, Measurement and Computing – Tsukuba.
    • This is really a quantum info./optics meeting, but it’s a big one and there’s usually some foundationsy talks as well.

    Personallly, I’ll definitely be at Vaxjo, Malta and Tsukuba, so I’ll see you there if you’re going.

    Foundations at APS

    I’m currently at the APS March Meeting, where there were two sessions on Quantum Foundations on Monday. I am pleased to report that they were well attended. Hopefully, this marks the start of an increased involvement of the APS in the field.

    The second session was particularly interesting, so here’s a short summary of what we heard:

    • Invited speaker Lucien Hardy outlined his Causaloid framework for general probabilistic theories without a fixed background causal structure. It is hoped that this might lead to a new path for developing a theory of quantum gravity.
    • Chris Fuchs gave a shortened version of his usual talk, focussing on the role of symmetric informationally complete POVMs in his approach to quantum foundations.
    • Terry Rudolph presented an extension of Rob Spekkens’ toy theory for dealing with continuous variable theories. This has lots of features in common with QM, but has a natural hidden variable interpretation, being a resticted version of Liouville mechanics.
    • Rob Spekkens showed how two seemingly different notions of “nonclassicallity”, nalely negativity of peseudo-probability distributions and the impossibility of a noncontextual hidden variable theory, are actually the same within the new approach to contextuality that he has developed.
    • Nicholas Harrigan outlined an approach to quantifying contextuality that he has been developing with Terry Rudolph.
    • Joseph Altepeter, from Kwiat’s group, gave an interesting presentation on their current state of the art photonic Bell inequality experiments.
    • OK, I have to admit that I was getting tired at this point and skipped out for a talk, so I have no idea about the next talk. Apologies to Giuliano Scarcelli.
    • There then followed two talks about decoherence from Diego Dalvit and Fernando Cucchietti, collaborators of Zurek and Paz respectively. This is an important topic for many interpretations of QM and the results looked solid. However, I’m not an expert on this stuff.
    • Ruth Kastner, who was due to deconstruct the now famous Ashfar experiment, was unfortunately unable to attend due to illness, but Ashfar was here to give his side of the story instead. The experiment is interesting at least because it has made quite a few physicists think about complimentarity and foundations in general a bit more deeply. Personally, I agree with Kastner’s analysis, but Ashfar disputes it.
    • Jeff Tollaksen outlined a new way of measuring the “weak values” introduced by Aharonov and collaborators. I didn’t follow the details of the construction, but look forward to reading the paper.
    • Caslav Brukner outlined his work with Zeilinger on an “information based” approach to quantum foundations. It’s not my personal favourite amongst such approaches, but gave plenty of food for thought.

    Well, foundations at this meeting are pretty much finished after that. There are still a few interesting quantum information sessions before the end of the week, but I can leave other bloggeurs to deal with that.

    Brainstorm for quantumfoundations.org

    Lucien Hardy informs me that he has purchased the internet domians www.quantumfoundations.org and www.quantumfoundations.com. The aim is to provide a central resource for the quantum foundations community, which is balanced (i.e. not biased towards a particular interpretation) and contains info on conferences, jobs, links to groups and researchers around the world etc. It would also be nice to have some original content, such as opinion pieces, as opposed to just links.

    Don’t expect the site to appear overnight, since it will probably take quite a while to get all the concepts together, do the web design, etc. However, if you have any ideas for the site then either contact Lucien or leave a comment below, which I will pass on.

    What is the point of Quantum Foundations?

    A couple of months ago, there was an interesting debate in the Quantum Foundations group here at PI, with the above title. Unfortunately, I missed it, but it is an interesting question given that QF is becoming increasingly popular amongst young physicists, whilst remaining a relatively obscure and controversial subject in most of the mainstream physics community. Here are 3 possible answers to the question:

    1. The goal of QF is to correctly predict the result of an experiment for which the standard approach to QM gives the wrong result. That is, we are in the business of providing alternative theories, that will eventually superseed QM. Work on things like spontaneous collapse models or nonlinear modifications to the Schroedinger equation falls into this category.
    2. The goal of QF is not to contradict QM within its domain of applicability, but it should suggest possible alterntive approaches in cases where we are currently uncertain how to go about applying quantum theory. The archetypal example of this is quantum gravity, although to be fair it is more common to hear foundations people give this response than to find them actually working on it. Notable exceptions are the work of Gell-Man, Hartle, Isham and collaborators, which draws on the Consistent Histories formalism, and the recent work of Lucien Hardy.
    3. The goal of QF is not to contradict QM at all, but it should suggest a variety of different ways to conceoptualize the subject, suggesting new possible experiments and theory that would have been difficult to imagine without considerable insight from QF. The main example we have of this is the field of quantum information. David Deutsch arrived at quantum computing by thinking about the many-worlds interpretation and Schumacher compression bears some similarity to the frequentist justifications of the quantum probability rule that began in Everett’s thesis. More recently, the Bayesian viewpoint of Caves, Fuchs, Schack, et. al. leads to new ways of doing quantum tomography and new variants of the quantum de-Finetti theorem, which have applications in quantum cryptography.
    4. The goal of QF is not to bother mainstream physics at all, but to come up with the most consistent and reasonable interpretation of QM possible, involving minimal unverifiable assumptions about the nature of reality.

    In my view, all four points of view can be justified. However, I think it is very useful to spell out exactly what we are up to to the rest of the world. A large portion of the physics community is skeptical about QF and, in my opinion, this is probably because they think we are all doing 1 or 4. If this were the case, I think I would agree with them, since QM has withstood a vast array of experimental tests and most of the alternatives suggested under category 1 seem contrived at best to me. Also, it is difficult to see what 4 could ever contribute to the rest of physics. It is also a problem that is better left to philosophers, since they are better qualified to tackle it.

    To me, 2 and 3 seem like the most promising avenues of research for physicists who are interested in the field.

    Support the APS topical group

    As you may know, the American Physical Society has recently opened a topical group on Quantum Information, Concepts and Compuation, which covers the foundations of quantum mechanics within its remit (under the “concepts” heading I suppose).  There will be a special session on the Foundations of Quantum Theory at the APS March Meeting in Baltimore this year.

    Although the abstract submission deadline has passed, I’d like to encourage everyone involved in quantum foundations to attend.  The APS has not always looked favourably on foundational studies and it has been difficult to get foundations papers published in their journals in the past.  The topical group could open the way for a new era of respectability for the subject within the APS, so making sure that the special session is well attended seems like a very good idea to me.  In any case, besides the political point, the talks are bound to be interesting.