The epistemic view of quantum states
Much of my foundations research at present explores the idea that the quantum state is a state of incomplete knowledge rather than a state of reality. Evidence for this idea can be found in a lot of recent work
in foundations. For a more precise definition of this distinction in the context of hidden variable theories, see
. I have written at some length (no doubt too much length) about a toy theory
which supports this thesis. I consider a classical theory that describes collections of 2-level systems (bits). I then impose a constraint on what any observer can know about the physical state of these systems and derive the features of the theory: which probability distribution over bit states can be prepared, which measurements can be implemented, etcetera. One might call such a theory an "epistemically-restricted statistical theory of bits". More recently, I have been considering epistemically-restricted theories for 3-level systems (trits) with student Olaf Schreiber and also for continuous variable systems with Steve Bartlett and Terry Rudolph.
One of the biggest challenges to the epistemic view of quantum states --and consequently one of the best clues for how to proceed with this research program-- lies with the phenomenon of contextuality, that is, the impossiblity of a noncontextual hidden variable model of quantum theory. I happen to think that the Kochen-Specker theorem is more significant than Bell's theorem (although I seem to be alone in this view).
In some recent work, I have tried to make the notion of contextuality
more operational and have also generalized it from sharp measurements to preparations, transformations and unsharp measurements. I've also got a bunch of unplublished results on this topic that I hope to get out soon.
Reference frames and superselection rules
My quantum information research recently has involved a fair number of projects concerning reference frames and superselection rules (typically in collaboration with Steve Bartlett, Terry Rudolph and others -- see the list of publications). Steve, Terry and I have recently written a review paper
on the subject. This topic has foundational significance, for instance, for the question of whether one can lift superselection rules
. It also sheds light on a recurrent controversy regarding whether quantum coherences are fact or fiction.
Interpretations of quantum mechanics
I am currently co-authoring a textbook with John Sipe on current interpretations of quantum mechanics. The working title is The Quantum Puzzle
The publisher is Oxford University Press. There are a few chapters left to be written and many to be revised.
Other topics I've been working on recently are:
- Complementarity between quantum error correction and quantum cryptography
- Quantum Bayes' theorem, quantum sufficient statistics, and pooling quantum states
- Uncertainty relations