Non-Classical Correlations in <i>n</i>-Cycle Setting
Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the cruci...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/2/134 |
| _version_ | 1798005639676428288 |
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| author | Kishor Bharti Maharshi Ray Leong-Chuan Kwek |
| author_facet | Kishor Bharti Maharshi Ray Leong-Chuan Kwek |
| author_sort | Kishor Bharti |
| collection | DOAJ |
| description | Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the <i>n</i>-cycle setting. In particular, we focus on correlations manifested by Kochen⁻Specker⁻Klyachko box (KS box), scenarios involving <i>n</i>-cycle non-contextuality inequalities and Popescu⁻Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary <i>n</i> dimension. The non-contextuality inequalities are analysed for <i>n</i>-cycle setting, and the condition for the quantum violation for odd as well as even <i>n</i>-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and <i>n</i>-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction. |
| first_indexed | 2024-04-11T12:42:36Z |
| format | Article |
| id | doaj.art-e4c8fe0ed2e4443ebd33fb68ec99afbf |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:42:36Z |
| publishDate | 2019-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e4c8fe0ed2e4443ebd33fb68ec99afbf2022-12-22T04:23:27ZengMDPI AGEntropy1099-43002019-02-0121213410.3390/e21020134e21020134Non-Classical Correlations in <i>n</i>-Cycle SettingKishor Bharti0Maharshi Ray1Leong-Chuan Kwek2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, SingaporeCentre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, SingaporeCentre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, SingaporeQuantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the <i>n</i>-cycle setting. In particular, we focus on correlations manifested by Kochen⁻Specker⁻Klyachko box (KS box), scenarios involving <i>n</i>-cycle non-contextuality inequalities and Popescu⁻Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary <i>n</i> dimension. The non-contextuality inequalities are analysed for <i>n</i>-cycle setting, and the condition for the quantum violation for odd as well as even <i>n</i>-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and <i>n</i>-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.https://www.mdpi.com/1099-4300/21/2/134KS BoxPR BoxNon-contextuality inequality |
| spellingShingle | Kishor Bharti Maharshi Ray Leong-Chuan Kwek Non-Classical Correlations in <i>n</i>-Cycle Setting Entropy KS Box PR Box Non-contextuality inequality |
| title | Non-Classical Correlations in <i>n</i>-Cycle Setting |
| title_full | Non-Classical Correlations in <i>n</i>-Cycle Setting |
| title_fullStr | Non-Classical Correlations in <i>n</i>-Cycle Setting |
| title_full_unstemmed | Non-Classical Correlations in <i>n</i>-Cycle Setting |
| title_short | Non-Classical Correlations in <i>n</i>-Cycle Setting |
| title_sort | non classical correlations in i n i cycle setting |
| topic | KS Box PR Box Non-contextuality inequality |
| url | https://www.mdpi.com/1099-4300/21/2/134 |
| work_keys_str_mv | AT kishorbharti nonclassicalcorrelationsininicyclesetting AT maharshiray nonclassicalcorrelationsininicyclesetting AT leongchuankwek nonclassicalcorrelationsininicyclesetting |