Communications in Mathematical Physics

, Volume 295, Issue 3, pp 829–851 | Cite as

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

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


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.


Entangle State Relative Entropy Separable State Quantum Operation Positive Partial Transpose 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Fernando G. S. L. Brandão
    • 1
    • 2
  • Martin B. Plenio
    • 1
    • 3
  1. 1.Institute of Mathematical Sciences and QOLS, Blackett LaboratoryImperial College LondonLondonUK
  2. 2.Departamento de FisicaUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  3. 3.Institut für Theoretische PhysikUniversität UlmUlmGermany

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