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Title: Uniqueness of all fundamental noncontextuality inequalities
Authors: Bharti, Kishor
Arora, Atul Singh
Kwek, Leong Chuan
Roland, Jérémie
Keywords: Science::Physics
Issue Date: 2020
Source: Bharti, K., Arora, A. S., Kwek, L. C. & Roland, J. (2020). Uniqueness of all fundamental noncontextuality inequalities. Physical Review Research, 2(3), 033010-1-033010-13.
Journal: Physical Review Research 
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.
ISSN: 2643-1564
DOI: 10.1103/PhysRevResearch.2.033010
Schools: School of Physical and Mathematical Sciences 
National Institute of Education 
Research Centres: MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654
Rights: © 2020 The Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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