A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/9/093001 |
| _version_ | 1797751202690105344 |
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| author | Xiao-Dong Yu Yan-Qing Guo D M Tong |
| author_facet | Xiao-Dong Yu Yan-Qing Guo D M Tong |
| author_sort | Xiao-Dong Yu |
| collection | DOAJ |
| description | Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem. |
| first_indexed | 2024-03-12T16:44:05Z |
| format | Article |
| id | doaj.art-fccfee25361741c6ae8c6f3df0a272b9 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:44:05Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-fccfee25361741c6ae8c6f3df0a272b92023-08-08T14:19:54ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117909300110.1088/1367-2630/17/9/093001A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequalityXiao-Dong Yu0Yan-Qing Guo1D M Tong2Department of Physics, Shandong University, Jinan 250100, People's Republic of ChinaDepartment of Physics, Dalian Maritime University, Dalian 116026, People's Republic of ChinaDepartment of Physics, Shandong University, Jinan 250100, People's Republic of ChinaQuantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem.https://doi.org/10.1088/1367-2630/17/9/093001Kochen-Specker theoremnoncontextuality inequalityquantum contextuality03.65.Ta03.65.Ud |
| spellingShingle | Xiao-Dong Yu Yan-Qing Guo D M Tong A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality New Journal of Physics Kochen-Specker theorem noncontextuality inequality quantum contextuality 03.65.Ta 03.65.Ud |
| title | A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality |
| title_full | A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality |
| title_fullStr | A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality |
| title_full_unstemmed | A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality |
| title_short | A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality |
| title_sort | proof of the kochen specker theorem can always be converted to a state independent noncontextuality inequality |
| topic | Kochen-Specker theorem noncontextuality inequality quantum contextuality 03.65.Ta 03.65.Ud |
| url | https://doi.org/10.1088/1367-2630/17/9/093001 |
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