Squashed entanglement in infinite dimensions

Shirokov, M. E.

doi:10.1063/1.4943598

Title: Squashed entanglement in infinite dimensions

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Abstract

We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.

Authors:

Shirokov, M. E. ^[1]

Steklov Mathematical Institute, Moscow (Russian Federation)

Publication Date:: Tue Mar 15 00:00:00 EDT 2016

OSTI Identifier:: 22597048

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 57; Journal Issue: 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; ENTROPY; MANY-DIMENSIONAL CALCULATIONS; QUANTUM ENTANGLEMENT

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                    Shirokov, M. E. Squashed entanglement in infinite dimensions.  United States: N. p., 2016. 
        Web.  doi:10.1063/1.4943598.

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                    Shirokov, M. E. Squashed entanglement in infinite dimensions.  United States.  https://doi.org/10.1063/1.4943598

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                    Shirokov, M. E. 2016.  
        "Squashed entanglement in infinite dimensions".  United States.  https://doi.org/10.1063/1.4943598.

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@article{osti_22597048,

  title        = {Squashed entanglement in infinite dimensions},

  author       = {Shirokov, M. E.},

  abstractNote = {We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.},

  doi          = {10.1063/1.4943598},

  url          = {https://www.osti.gov/biblio/22597048},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 3,

  volume       = 57,

  place        = {United States},

  year         = {Tue Mar 15 00:00:00 EDT 2016},

  month        = {Tue Mar 15 00:00:00 EDT 2016}

}

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