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arXiv · 1412.5213

A classification of multipartite states by degree of non-locality

Samson Abramsky·Carmen Constantin
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Abstract

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.

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Samson Abramsky, Carmen Constantin. 2014-12-30. A classification of multipartite states by degree of non-locality. https://doi.org/10.4204/eptcs.171.2

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