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

Brandão, Fernando G. S. L. and Plenio, Martin B. (2010) A Reversible Theory of Entanglement and its Relation to the Second Law. Communications in Mathematical Physics, 295 (3). pp. 829-851. ISSN 0010-3616. doi:10.1007/s00220-010-1003-1.

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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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Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2010 Springer-Verlag. Received: 5 March 2009; Accepted: 4 August 2009; Published online: 18 February 2010. We gratefully acknowledge Koenraad Audenaert, Jens Eisert, Andrzej Grudka, Michał Horodecki, Ryszard Horodecki, Shashank Virmani, Reinhard Werner, Andreas Winter, and the participants in the 2009 McGill-Bellairs workshop formany interesting discussions and useful correspondences. This work is part of the QIP-IRC supported by EPSRC (GR/S82176/0) as well as the Integrated Project Qubit Applications (QAP) supported by the IST directorate as Contract Number 015848 and was supported by the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), an EPSRC Postdoctoral Fellowship for Theoretical Physics and a Royal Society Wolfson Research Merit Award.
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Engineering and Physical Sciences Research Council (EPSRC)GR/S82176/0
IST directorate015848
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)UNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20160526-104144804
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67386
Deposited By: Tony Diaz
Deposited On:26 May 2016 19:12
Last Modified:11 Nov 2021 00:31

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