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A Reversible Theory of Entanglement and its Relation to the Second Law

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Abstract

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement.

Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein’s Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.

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Authors and Affiliations

  1. Institute of Mathematical Sciences and QOLS, Blackett Laboratory, Imperial College London, London, SW7 2BW, UK

    Fernando G. S. L. Brandão & Martin B. Plenio

  2. Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, MG, 30123-970, Brazil

    Fernando G. S. L. Brandão

  3. Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany

    Martin B. Plenio

Authors
  1. Fernando G. S. L. Brandão
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  2. Martin B. Plenio
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Correspondence to Fernando G. S. L. Brandão.

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Communicated by M.B. Ruskai

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Brandão, F.G.S.L., Plenio, M.B. A Reversible Theory of Entanglement and its Relation to the Second Law. Commun. Math. Phys. 295, 829–851 (2010). https://doi.org/10.1007/s00220-010-1003-1

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  • DOI: https://doi.org/10.1007/s00220-010-1003-1

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