2015/02/28 by Samson Abramsky, Rui Soares Barbosa, Kohei Kishida +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #cs.LO #math.AT #quant-ph
paper · pdf · doi:10.4230/lipics.csl.2015.211
published as 24th EACSL Annual Conference on Computer Science Logic (CSL 2015), Leibniz International Proceedings in Informatics (LIPIcs), 41: 211-228, 2015 · 18 pages, 4 figures
arxiv created 2017/03/05 · arxiv updated 2018/07/03
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.