A Classification of Multipartite States by Degree of Non-Locality

Samson Abramsky, Carmen Maria Constantin

Published 2014-12-16Version 1

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.