Physics – Quantum Physics
Scientific paper
2011-02-01
New Journal of Physics 13 (2011) 113036
Physics
Quantum Physics
33 pages. Extensively revised, new results included. Published in New Journal of Physics
Scientific paper
10.1088/1367-2630/13/11/113036
We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples --- due to Bell, Hardy, and Greenberger, Horne and Zeilinger, respectively --- occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for Kochen-Specker type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the `parity proofs' commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product.
Abramsky Samson
Brandenburger Adam
No associations
LandOfFree
The Sheaf-Theoretic Structure Of Non-Locality and Contextuality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Sheaf-Theoretic Structure Of Non-Locality and Contextuality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Sheaf-Theoretic Structure Of Non-Locality and Contextuality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-79032