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Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

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Abstract

Let ρ 12 be a bipartite density matrix. We prove lower bounds for the entanglement of formation Ef(ρ 12) and the squashed entanglement Esq(ρ 12) in terms of the conditional entropy S 12 − S 1 and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

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Authors and Affiliations

  1. Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Eric A. Carlen

  2. Departments of Mathematics and Physics, Jadwin Hall, Princeton University, P. O. Box 708, Princeton, NJ, 08542, USA

    Elliott H. Lieb

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  1. Eric A. Carlen
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  2. Elliott H. Lieb
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Correspondence to Elliott H. Lieb.

Additional information

We dedicate this paper to Walter Thirring on the occasion of his 85th birthday

E. A. Carlen’s work partially supported by U.S. National Science Foundation grant DMS 0901632 and E. H. Lieb’s work partially supported by U.S. National Science Foundati grant PHY 0965859.

© 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.

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Carlen, E.A., Lieb, E.H. Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy. Lett Math Phys 101, 1–11 (2012). https://doi.org/10.1007/s11005-012-0565-6

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  • DOI: https://doi.org/10.1007/s11005-012-0565-6

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