Fundamental work costs of preparation and erasure in the presence of quantum side information

2025-03-12

AI Summary

This work investigates the single-shot work cost limits for state preparation and erasure in thermodynamic systems with quantum side information. Methodologically, it establishes a thermodynamic framework for quantum Maxwell’s demons by integrating quantum resource theory with single-shot information theory. It first endows smooth min/max conditional entropies with explicit operational thermodynamic interpretations at the microscopic level. The authors rigorously prove the axiomatic maximality of the conditional max-entropy and derive a second law of thermodynamics expressed as a quantum side-information–enhanced conditional Helmholtz free energy. As a result, they obtain tight analytical expressions for the single-shot work cost of preparation and erasure under arbitrary Hamiltonians. These results unify the physical interpretations of various conditional entropies and establish the precise correction to the macroscopic second law of thermodynamics induced by quantum side information.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The thought experiment of Maxwell's demon highlights the effect of side information in thermodynamics. In this paper, we present an axiomatic treatment of a quantum Maxwell's demon, by introducing a resource-theoretic framework of quantum thermodynamics in the presence of quantum side information. Under minimal operational assumptions that capture the demon's behaviour, we derive the one-shot work costs of preparing, as well as erasing, a thermodynamic system whose coupling with the demon's mind is described by a bipartite quantum state. With trivial Hamiltonians, these work costs are precisely captured by the smoothed conditional min- and max-entropies, respectively, thus providing operational interpretations for these one-shot information-theoretic quantities in microscopic thermodynamics. An immediate, information-theoretic implication of our results is an affirmative proof of the conjectured maximality of the conditional max-entropy among all axiomatically plausible conditional entropies, complementing the recently established minimality of the conditional min-entropy. We then generalize our main results to the setting with nontrivial Hamiltonians, wherein the work costs of preparation and erasure are captured by a generalized type of mutual information. Finally, we present a macroscopic second law of thermodynamics in the presence of quantum side information, in terms of a conditional version of the Helmholtz free energy. Our results extend the conceptual connection between thermodynamics and quantum information theory by refining the axiomatic common ground between the two theories and revealing fundamental insights of each theory in light of the other.

Problem

• Quantifies work costs in quantum thermodynamics with side information.
• Derives operational interpretations for one-shot information-theoretic quantities.
• Extends thermodynamics laws to include quantum side information effects.

Innovation

• Resource-theoretic framework for quantum thermodynamics
• One-shot work costs using smoothed entropies
• Generalized mutual information for nontrivial Hamiltonians