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Contextuality, Cohomology and Paradox

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arxiv 1502.03097 v2 pith:RU4QRWJX submitted 2015-02-10 quant-ph cs.LOmath.AT

classification quant-phcs.LOmath.AT
keywords contextualityquantumtheoryimportantabramskyall-vs-nothingargumentsbrandenburger
verification ladder T0 review T1 audit T2 compute T3 formal
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Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.

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