Smallest state spaces for which bipartite entangled quantum states are separable
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general s...
| 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/10.1088/1367-2630/17/9/093047 |
| _version_ | 1797751133027958784 |
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| author | Hussain Anwar Sania Jevtic Oliver Rudolph Shashank Virmani |
| author_facet | Hussain Anwar Sania Jevtic Oliver Rudolph Shashank Virmani |
| author_sort | Hussain Anwar |
| collection | DOAJ |
| description | According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only a restricted set of measurements is available. With these motivations in mind, we ask what are the smallest sets of local operators such that a pure bipartite entangled quantum state becomes separable? We find that in the case of maximally entangled states there are many inequivalent solutions, including for example the sets of phase point operators that arise in the study of discrete Wigner functions. We therefore provide a new way of interpreting these operators, and more generally, provide an alternative method for constructing local hidden variable models for entangled quantum states under subsets of quantum measurements. |
| first_indexed | 2024-03-12T16:44:01Z |
| format | Article |
| id | doaj.art-e6de546f3c4547a9920c2c058782ac3c |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:44:01Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e6de546f3c4547a9920c2c058782ac3c2023-08-08T14:21:28ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117909304710.1088/1367-2630/17/9/093047Smallest state spaces for which bipartite entangled quantum states are separableHussain Anwar0Sania Jevtic1Oliver Rudolph2Shashank Virmani3Department of Mathematical Sciences , Brunel University, Uxbridge, Middlesex UB8 3PH, UK; Department of Physics , Imperial College London, London SW7 2AZ, UKDepartment of Mathematical Sciences , Brunel University, Uxbridge, Middlesex UB8 3PH, UK; Institut für Theoretische Physik , Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, GermanyLeonardo da Vinci Gymnasium , Im Spitzerfeld 25, 69151 Neckargemünd, Germany & Hector-Seminar, Waldhoferstr. 100, 69123 Heidelberg, GermanyDepartment of Mathematical Sciences , Brunel University, Uxbridge, Middlesex UB8 3PH, UKAccording to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only a restricted set of measurements is available. With these motivations in mind, we ask what are the smallest sets of local operators such that a pure bipartite entangled quantum state becomes separable? We find that in the case of maximally entangled states there are many inequivalent solutions, including for example the sets of phase point operators that arise in the study of discrete Wigner functions. We therefore provide a new way of interpreting these operators, and more generally, provide an alternative method for constructing local hidden variable models for entangled quantum states under subsets of quantum measurements.https://doi.org/10.1088/1367-2630/17/9/093047bipartite entangled stateslocal hidden variablesseparabilityprojective tensor normdiscrete wigner function03.67.-a |
| spellingShingle | Hussain Anwar Sania Jevtic Oliver Rudolph Shashank Virmani Smallest state spaces for which bipartite entangled quantum states are separable New Journal of Physics bipartite entangled states local hidden variables separability projective tensor norm discrete wigner function 03.67.-a |
| title | Smallest state spaces for which bipartite entangled quantum states are separable |
| title_full | Smallest state spaces for which bipartite entangled quantum states are separable |
| title_fullStr | Smallest state spaces for which bipartite entangled quantum states are separable |
| title_full_unstemmed | Smallest state spaces for which bipartite entangled quantum states are separable |
| title_short | Smallest state spaces for which bipartite entangled quantum states are separable |
| title_sort | smallest state spaces for which bipartite entangled quantum states are separable |
| topic | bipartite entangled states local hidden variables separability projective tensor norm discrete wigner function 03.67.-a |
| url | https://doi.org/10.1088/1367-2630/17/9/093047 |
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