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...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/160732 |
| _version_ | 1826127925049556992 |
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| author | Bharti, Kishor Arora, Atul Singh Kwek, Leong Chuan Roland, Jérémie |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bharti, Kishor Arora, Atul Singh Kwek, Leong Chuan Roland, Jérémie |
| author_sort | Bharti, Kishor |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:16:52Z |
| format | Journal Article |
| id | ntu-10356/160732 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:16:52Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1607322023-02-28T20:08:29Z Uniqueness of all fundamental noncontextuality inequalities Bharti, Kishor Arora, Atul Singh Kwek, Leong Chuan Roland, Jérémie School of Physical and Mathematical Sciences National Institute of Education MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654 Science::Physics Graph Theoretic Approach ITS Applications 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. Ministry of Education (MOE) National Research Foundation (NRF) Published version A.S.A. and J.R. acknowledge financial support from the Belgian Fonds de la Recherche Scientifique (FNRS) under Grants No. F.4515.16 (QUICTIME) and No. R.50.05.18.F (QuantAlgo). A.S.A. further acknowledges the FNRS for support through Grant No. F3/5/5–MCF/XH/FC– 16749 FRIA. K.B. acknowledges the Centre for Quantum Technologies (CQT) Graduate Scholarship. K.B. and L.C.K. are grateful to the National Research Foundation and the Ministry of Education, Singapore for financial support. 2022-08-02T00:49:12Z 2022-08-02T00:49:12Z 2020 Journal Article 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. https://dx.doi.org/10.1103/PhysRevResearch.2.033010 2643-1564 https://hdl.handle.net/10356/160732 10.1103/PhysRevResearch.2.033010 2-s2.0-85115898527 3 2 033010-1 033010-13 en Physical Review Research © 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. application/pdf |
| spellingShingle | Science::Physics Graph Theoretic Approach ITS Applications Bharti, Kishor Arora, Atul Singh Kwek, Leong Chuan Roland, Jérémie Uniqueness of all fundamental noncontextuality inequalities |
| title | Uniqueness of all fundamental noncontextuality inequalities |
| title_full | Uniqueness of all fundamental noncontextuality inequalities |
| title_fullStr | Uniqueness of all fundamental noncontextuality inequalities |
| title_full_unstemmed | Uniqueness of all fundamental noncontextuality inequalities |
| title_short | Uniqueness of all fundamental noncontextuality inequalities |
| title_sort | uniqueness of all fundamental noncontextuality inequalities |
| topic | Science::Physics Graph Theoretic Approach ITS Applications |
| url | https://hdl.handle.net/10356/160732 |
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