Second Law of Entanglement Manipulation with Entanglement Battery

TL;DR

This paper demonstrates that with an entanglement battery, arbitrary mixed state entanglement transformations can be made reversible, establishing a second law-like principle for entanglement manipulation and resolving a long-standing open question.

Contribution

It introduces the concept of an entanglement battery enabling reversible entanglement transformations, extending the second law of entanglement manipulation to mixed states.

Findings

Reversible entanglement transformations are possible with an entanglement battery.

The transformation rate is given by a ratio of entanglement measures.

The framework applies to multipartite entanglement and quantum thermodynamics.

Abstract

A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic regime, mirroring the reversible nature of Carnot cycles in classical thermodynamics. While a conclusive proof of this conjecture has been missing so far, earlier studies have excluded reversible entanglement manipulation in various settings. In this work, we show that arbitrary mixed state entanglement transformations can be made reversible under local operations and classical communication, when assisted by an entanglement battery--an auxiliary quantum system that stores and supplies entanglement in a way that ensures no net entanglement is lost. In particular, the rate of transformation in the asymptotic limit can be quantitatively expressed as a ratio of entanglement present within the quantum states involved. Our setting allows to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a ``second law'' of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.