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A Necessary and Sufficient Criterion for the Separability of Quantum State

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficie...

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Autores principales: Li, Jun-Li, Qiao, Cong-Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5780502/
https://www.ncbi.nlm.nih.gov/pubmed/29362415
http://dx.doi.org/10.1038/s41598-018-19709-z
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author Li, Jun-Li
Qiao, Cong-Feng
author_facet Li, Jun-Li
Qiao, Cong-Feng
author_sort Li, Jun-Li
collection PubMed
description Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn’s problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.
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spelling pubmed-57805022018-02-06 A Necessary and Sufficient Criterion for the Separability of Quantum State Li, Jun-Li Qiao, Cong-Feng Sci Rep Article Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn’s problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state. Nature Publishing Group UK 2018-01-23 /pmc/articles/PMC5780502/ /pubmed/29362415 http://dx.doi.org/10.1038/s41598-018-19709-z Text en © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Li, Jun-Li
Qiao, Cong-Feng
A Necessary and Sufficient Criterion for the Separability of Quantum State
title A Necessary and Sufficient Criterion for the Separability of Quantum State
title_full A Necessary and Sufficient Criterion for the Separability of Quantum State
title_fullStr A Necessary and Sufficient Criterion for the Separability of Quantum State
title_full_unstemmed A Necessary and Sufficient Criterion for the Separability of Quantum State
title_short A Necessary and Sufficient Criterion for the Separability of Quantum State
title_sort necessary and sufficient criterion for the separability of quantum state
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5780502/
https://www.ncbi.nlm.nih.gov/pubmed/29362415
http://dx.doi.org/10.1038/s41598-018-19709-z
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