Squashed entanglement in infinite dimensions

Journal Article · Tue Mar 15 04:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4943598· OSTI ID:22597048

Shirokov, M. E. ^[1]

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1. Steklov Mathematical Institute, Moscow (Russian Federation)

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.

• OSTI ID: 22597048
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 57; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
ENTROPY
MANY-DIMENSIONAL CALCULATIONS
QUANTUM ENTANGLEMENT