Entanglement Theory and the Second Law of Thermodynamics

TL;DR

This paper explores the deep connection between entanglement theory and thermodynamics, proposing a reversible framework using non-entangling transformations and the asymptotic relative entropy of entanglement.

Contribution

It introduces a reversible entanglement theory based on non-entangling transformations and establishes a rigorous link with thermodynamics using the asymptotic relative entropy of entanglement.

Findings

Reversible entanglement theory is possible with non-entangling transformations.

The asymptotic relative entropy of entanglement plays a role analogous to entropy in thermodynamics.

The approach extends to general resource theories and quantum information science.

Abstract

Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws, such as the non-increase of entanglement under local operations, that govern its manipulation and aims to draw from them formal analogies to the second law of thermodynamics. However, while in the second law the entropy uniquely determines whether a state is adiabatically accessible from another, the manipulation of entanglement under local operations exhibits a fundamental irreversibility which prevents the existence of such an order. Here we show that a reversible theory of entanglement and a rigorous relationship with thermodynamics may be established when one considers all non-entangling transformations. The role of the entropy in the second law is taken by the asymptotic relative entropy of entanglement in the basic law of entanglement. We show the usefulness of this new approach to general resource theories and to quantum information theory.