English

Contextuality, Cohomology and Paradox

Quantum Physics 2018-07-03 v2 Logic in Computer Science Algebraic Topology

Abstract

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.

Keywords

Cite

@article{arxiv.1502.03097,
  title  = {Contextuality, Cohomology and Paradox},
  author = {Samson Abramsky and Rui Soares Barbosa and Kohei Kishida and Raymond Lal and Shane Mansfield},
  journal= {arXiv preprint arXiv:1502.03097},
  year   = {2018}
}

Comments

18 pages, 4 figures

R2 v1 2026-06-22T08:27:05.364Z