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Testing the equivalence to thermal states via extractable work under LOCC

Toshihiro Yada, Nobuyuki Yoshioka, Takahiro Sagawa

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.

Testing the equivalence to thermal states via extractable work under LOCC

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.
Paper Structure (1 section, 3 theorems, 18 equations, 2 figures, 1 table)

This paper contains 1 section, 3 theorems, 18 equations, 2 figures, 1 table.

Table of Contents

  1. Derivation of Eq. \ref{['eq:W_LOCC_UB']}

Key Result

Theorem 1

For a Haar-random $N$-qubit pure state $\ket{\psi}$, we have with high probability.

Figures (2)

  • Figure 1: Schematics of work extraction under (a) arbitrary global operations, (b) LOCC, and (c) strictly local operations. The increase in extractable work from local operations to LOCC reflects the contribution of classically accessible multipartite correlations, whereas the gap between global operations and LOCC quantifies multipartite quantum correlations.
  • Figure 2: Schematic for an $L$-round LOCC protocol. The local operation in the $l$-th round can be adaptively changed depending on the past measurement outcomes $Y^{l-1}$. The net work extraction through the LOCC protocol consists of two contributions: the extractable work from each local subsystem and the work cost of memory erasure.

Theorems & Definitions (3)

  • Theorem 1: Haar-random states, informal
  • Theorem 2: Approximate $t$-designs, informal
  • Theorem 3: Random graph states, informal