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      On the Cohomology of Contextuality

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          Abstract

          Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of global sections. In the present work, we illustrate new insights into different aspects of this theory. We shed light on the power of detection of the cohomological obstruction by showing that it is not a complete invariant for strong contextuality even under symmetry and connectedness restrictions on the measurement cover, disproving a previous conjecture. We generalise obstructions to higher cohomology groups and show that they give rise to a refinement of the notion of cohomological contextuality: different "levels" of contextuality are organised in a hierarchy of logical implications. Finally, we present an alternative description of the first cohomology group in terms of torsors, resulting in a new interpretation of the cohomological obstructions.

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          Most cited references18

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          Quantum nonlocality as an axiom

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            Simple unified form for the major no-hidden-variables theorems.

            Mermin (1990)
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              • Record: found
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              Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories.

              (1992)
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                Author and article information

                Journal
                2017-01-03
                Article
                10.4204/EPTCS.236.2
                1701.00656
                4ff579f8-6560-4d0b-a6ac-8829da614b9d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                EPTCS 236, 2017, pp. 21-39
                In Proceedings QPL 2016, arXiv:1701.00242
                quant-ph cs.LO
                EPTCS

                Quantum physics & Field theory,Theoretical computer science
                Quantum physics & Field theory, Theoretical computer science

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