A classification of multipartite states by degree of non-locality

Samson Abramsky
(University of Oxford)
Carmen Constantin
(University of Oxford)

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.

In Bob Coecke and Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL 2013), Castelldefels (Barcelona), Spain, 17th to 19th July 2013, Electronic Proceedings in Theoretical Computer Science 171, pp. 10–25.
Published: 27th December 2014.

ArXived at: https://dx.doi.org/10.4204/EPTCS.171.2 bibtex PDF
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