Uniqueness of all fundamental noncontextuality inequalities
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...
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| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/160732 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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