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.
Highlights
We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle
In an attempt to conceptually understand the departure of the predictions of quantum mechanics (QM) from that of classical physics, the notion of contextuality was introduced
It is one of the most general ways of capturing this divergence [1,2]; the celebrated Bell nonlocality can be viewed as a special case of contextuality where the context is provided via spacelike separation of the parties involved [3,4]
Summary
In an attempt to conceptually understand the departure of the predictions of quantum mechanics (QM) from that of classical physics, the notion of contextuality was introduced. It is one of the most general ways of capturing this divergence [1,2]; the celebrated Bell nonlocality can be viewed as a special case of contextuality where the context is provided via spacelike separation of the parties involved [3,4]. Bell nonlocality has found many applications in quantum key distribution [5], randomness certification [6], self-testing [7,8,9], and distributed computing [10], to name a few [11]. It has been uncovered to be the resource powering the measurement based model and a class of fault tolerant models of quantum computation [16,17], among others [1,16,17,18,19,20,21,22,23]
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