Thermodynamics of bipartite entanglement

TL;DR

This paper reviews the thermodynamical structure of bipartite entanglement, comparing finite and asymptotic cases, and explores the second law under different quantum operations.

Contribution

It demonstrates the formal inequivalence of thermodynamics and entanglement theory for finite systems and establishes their full equivalence in the asymptotic limit for pure states.

Findings

Finite systems show formal inequivalence between thermodynamics and entanglement.

Asymptotic pure states exhibit full equivalence between the two theories.

Different methods for the second law are applied to mixed states with specific quantum operations.

Abstract

A review is given on the thermodynamical structure of bipartite entanglement. By comparing it to the axiomatic formulation of thermodynamics presented by Giles it is shown that for finite dimensional systems the two theories are formally inequivalent. The same approach is used to demonstrate the full equivalence in the asymptotic limit for pure quantum states. For mixed states a different method for obtaining the second law is described applied to two different classes of operations, PPT-preserving and asymptotically non-entangling operations.