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Complete characterisation of state conversions by work extraction

Chung-Yun Hsieh, Manuel Gessner

TL;DR

This work introduces a thermodynamic work-extraction task that encodes energy-storage enhancement $\Delta(\rho,H)$ to completely determine state conversions under general quantum resource theories via $\Delta_{\mathcal{O}_R}(\rho,H)$. The central result states that $\rho \stackrel{\mathcal{O}_R}{\longrightarrow} \sigma$ if and only if $\Delta_{\mathcal{O}_R}(\rho,H) \ge \Delta_{\mathcal{O}_R}(\sigma,H)$ for all bounded $H$, connecting resource conversion to a family of Hamiltonians. Applied to informational non-equilibrium, the framework recovers majorisation for unital (mixed-unitary) channels and yields a thermodynamic form of Nielsen’s theorem for LOCC in entanglement theory, while also establishing a thermodynamic universal certification class (URCC) and a quantifiable resource measure via work extraction. The results illuminate how energy-storage processes can operationally certify and quantify general quantum resources and suggest new practical avenues for quantum batteries and thermodynamic tasks beyond ergotropy-based approaches.

Abstract

We introduce a thermodynamic work extraction task that describes the energy storage enhancement of quantum systems, which is naturally related to quantum battery's charging process. This task induces majorisation-like conditions that provide a necessary and sufficient characterisation of state conversions in general quantum resource theories. When applied to specific resources, these conditions reduce to the majorisation conditions under unital channels and provide a thermodynamic version of Nielsen's theorem in entanglement theory. We show how this result establishes the first universal resource certification class based on thermodynamics, and how it can be employed to quantify general quantum resources based on work extraction.

Complete characterisation of state conversions by work extraction

TL;DR

This work introduces a thermodynamic work-extraction task that encodes energy-storage enhancement to completely determine state conversions under general quantum resource theories via . The central result states that if and only if for all bounded , connecting resource conversion to a family of Hamiltonians. Applied to informational non-equilibrium, the framework recovers majorisation for unital (mixed-unitary) channels and yields a thermodynamic form of Nielsen’s theorem for LOCC in entanglement theory, while also establishing a thermodynamic universal certification class (URCC) and a quantifiable resource measure via work extraction. The results illuminate how energy-storage processes can operationally certify and quantify general quantum resources and suggest new practical avenues for quantum batteries and thermodynamic tasks beyond ergotropy-based approaches.

Abstract

We introduce a thermodynamic work extraction task that describes the energy storage enhancement of quantum systems, which is naturally related to quantum battery's charging process. This task induces majorisation-like conditions that provide a necessary and sufficient characterisation of state conversions in general quantum resource theories. When applied to specific resources, these conditions reduce to the majorisation conditions under unital channels and provide a thermodynamic version of Nielsen's theorem in entanglement theory. We show how this result establishes the first universal resource certification class based on thermodynamics, and how it can be employed to quantify general quantum resources based on work extraction.
Paper Structure (18 sections, 5 theorems, 34 equations, 2 figures)

This paper contains 18 sections, 5 theorems, 34 equations, 2 figures.

Table of Contents

  1. Preliminary Notions
  2. Quantum resource theories
  3. Working Hypotheses
  4. Results
  5. Conversion problem in resource theories
  6. Energy storage enhancement as a work extraction task and its relation with quantum batteries
  7. Completely characterising state conversion by work extraction
  8. Implication for informational thermodynamics and entanglement
  9. Witnessing and quantifying quantum resources by work extraction
  10. Implications to quantum batteries
  11. Conclusions
  12. Acknowledgements
  13. Appendix
  14. Appendix A: On the convexity and compactness of $\mathcal{F}_{R}$
  15. Appendix B: Proof of Theorem \ref{['Result:conversion']}
  16. ...and 3 more sections

Key Result

Theorem 1

Let $0\le\epsilon<\delta$ be fixed energy scales. Then $\rho\stackrel{\mathcal{O}_R}{\longrightarrow}\sigma$ if and only if

Figures (2)

  • Figure 1: Schematic illustration of the central question.We ask whether any class of work extraction tasks can completely characterise state conversions in general resource theories. A suitable answer can offer a method to analyse a broad range of quantum effects via quantum batteries.
  • Figure 2: Work extraction task that describes energy storage enhancement. Each round starts with the same initial state $\rho$ subject to a fully degenerate initial Hamiltonian. If we extract work with this setting, we obtain $W_{\rm inf}(\rho)$ [Eq. \ref{['Eq:Winf def']}]. Alternatively, if we quench the Hamiltonian into a new one, $H$, and then perform work extraction, we obtain $W(\rho,H)$ [Eq. \ref{['Eq:W def']}]. The energy storage change$\Delta(\rho,H)$is the difference between these two work values.

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • proof
  • proof
  • Lemma 5
  • proof
  • proof
  • proof