Uniqueness of all fundamental noncontextuality inequalities

• Main Authors: Bharti, Kishor, Arora, Atul Singh, Kwek, Leong Chuan, Roland, Jérémie
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Physics; Graph Theoretic Approach; ITS Applications
• Online Access: https://hdl.handle.net/10356/160732
• Institution: Nanyang Technological University

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.