Testing the equivalence to thermal states via extractable work under LOCC

TL;DR

This paper investigates when pure quantum many-body states behave thermally under LOCC, revealing that multipartite entanglement structure determines their work extraction capabilities and refining the concept of thermal equivalence.

Contribution

It establishes criteria for thermal equivalence of pure states under LOCC, linking this property to their multipartite quantum correlations and entanglement structure.

Findings

Haar-random states cannot yield extensive work under LOCC.

Graph states with limited entanglement can still allow extensive work extraction.

Thermal equivalence depends on multipartite quantum correlation structure.

Abstract

Understanding the thermal behavior of quantum many-body pure states is one of the most fundamental issues in quantum thermodynamics. It is widely known that typical pure states yield vanishing work, just as thermal states do, when one restricts to local operations that cannot access correlations among subsystems. However, it remains unclear whether this equivalence to thermal states persists under LOCC (local operations and classical communication), where classically accessible correlations can be exploited for work extraction. In this work, we establish criteria for determining whether many-body pure states remain equivalent to thermal states even under LOCC, and show that this thermal equivalence is governed by their multipartite quantum correlation structure. We show that states with asymptotically maximal multipartite entanglement, such as Haar-random states, cannot yield extensive work under LOCC, whereas some states with limited multipartite entanglement, such as constant-degree graph states, allow extensive work extraction despite being locally indistinguishable from thermal states. Thus, our work provides a refined operational notion of thermal equivalence beyond the traditional local regime, which is becoming increasingly important due to the recent expansion of experimentally accessible operations.