A reversible theory of entanglement and its relation to the second law

TL;DR

This paper proves that in the asymptotic limit, entanglement can be reversibly converted between different forms, with the regularized relative entropy of entanglement serving as the unique measure, linking quantum information and thermodynamics.

Contribution

It provides a rigorous proof that the regularized relative entropy of entanglement is the unique measure for reversible entanglement manipulation in the asymptotic limit.

Findings

Entanglement can be reversibly interconverted asymptotically.

The regularized relative entropy of entanglement is the unique measure.

Connection established between entanglement theory and the second law of thermodynamics.

Abstract

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and 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 proved in [Brandao and Plenio, Commun. Math. 295, 791 (2010)], 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.