All fundamental non-contextuality inequalities are unique
Abstract
Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [PRA 88, 032104 (2013); Annals of mathematics, 51-299 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anti-cyclically exclusive. Thus, the non-contextuality inequalities whose underlying exclusivity structure is as stated, either cyclic or anti-cyclic, are fundamental to quantum theory. We show that there is a unique non-contextuality inequality for each non-trivial cycle and anti-cycle. In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.
Cite
@article{arxiv.1811.05294,
title = {All fundamental non-contextuality inequalities are unique},
author = {Kishor Bharti and Atul Singh Arora and Leong Chuan Kwek and Jérémie Roland},
journal= {arXiv preprint arXiv:1811.05294},
year = {2020}
}
Comments
17 pages (5 main, 12 appendix), 4 figures; In v2, generalised the result, upgraded the title, clarified the relation to prior work and rewrote the narrative