2014/12/30 by Samson Abramsky, Carmen Constantin
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.4204/eptcs.171.2
published as EPTCS 171, 2014, pp. 10-25 · In Proceedings QPL 2013, arXiv:1412.7917
arxiv created 2014/12/30 · arxiv updated 2014/12/31
We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky and Brandenburger: strong contextuality, logical contextuality, and probabilistic contextuality. We study n-qubit pure states. We conjecture that for more than 2 parties, all entangled states are logically contextual. We prove a number of results in support of this conjecture: (1) We show that all permutation-symmetric states are logically non-local. (2) We study the class of balanced states with functional dependencies. These states are described by Boolean functions and have a rich structure, allowing a detailed analysis, which again confirms the conjecture in this case.