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Robustness as a thermodynamic currency: work advantages and preparation costs of nonclassical states

Luis Pedro Garcıa-Pintos, Tanmoy Biswas, Chandan Datta

Abstract

Understanding whether uniquely quantum features can provide concrete advantages in thermodynamic processes is a central objective of quantum thermodynamics. A key challenge is quantifying how different forms of non-classicality can be systematically harnessed to enhance thermodynamic tasks. In light of this, we prove that any form of non-classicality can serve as a thermodynamic resource. In particular, any system that possesses quantum magic, coherence, or non-classical correlations can be leveraged to extract higher amounts of work than if the system does not possess such resources. The quantum thermodynamic advantages--quantified by the ratio between work extractable from a resource state and work extractable in its absence--increase with the resource robustness. We show that for any convex quantum resource theory, any resourceful state can yield a work-extraction advantage over all free states via a cyclic quench/thermalization protocol whose Hamiltonian is engineered from an optimal robustness witness. We illustrate concrete examples in which the robustness measures increase with the system's dimension, yielding quantum thermodynamic advantages that scale with it. In contrast, we also show that preparing a resource state (e.g., one with magic, coherence, or non-classical correlations) can be significantly more thermodynamically costly than preparing any state without such a resource. Concretely, there always exists a protocol that can prepare any non-resourceful state at significantly less work than it takes to prepare a resourceful state. Overall, our results provide operational meaning to robustness measures of quantum resources in terms of their thermodynamic costs and advantages.

Robustness as a thermodynamic currency: work advantages and preparation costs of nonclassical states

Abstract

Understanding whether uniquely quantum features can provide concrete advantages in thermodynamic processes is a central objective of quantum thermodynamics. A key challenge is quantifying how different forms of non-classicality can be systematically harnessed to enhance thermodynamic tasks. In light of this, we prove that any form of non-classicality can serve as a thermodynamic resource. In particular, any system that possesses quantum magic, coherence, or non-classical correlations can be leveraged to extract higher amounts of work than if the system does not possess such resources. The quantum thermodynamic advantages--quantified by the ratio between work extractable from a resource state and work extractable in its absence--increase with the resource robustness. We show that for any convex quantum resource theory, any resourceful state can yield a work-extraction advantage over all free states via a cyclic quench/thermalization protocol whose Hamiltonian is engineered from an optimal robustness witness. We illustrate concrete examples in which the robustness measures increase with the system's dimension, yielding quantum thermodynamic advantages that scale with it. In contrast, we also show that preparing a resource state (e.g., one with magic, coherence, or non-classical correlations) can be significantly more thermodynamically costly than preparing any state without such a resource. Concretely, there always exists a protocol that can prepare any non-resourceful state at significantly less work than it takes to prepare a resourceful state. Overall, our results provide operational meaning to robustness measures of quantum resources in terms of their thermodynamic costs and advantages.
Paper Structure (4 sections, 5 theorems, 32 equations, 1 figure)

This paper contains 4 sections, 5 theorems, 32 equations, 1 figure.

Table of Contents

  1. Thermodynamic advantages from quantum resources
  2. Work extraction from resource states
  3. Thermodynamic costs of quantum resources
  4. Discussion

Key Result

Theorem 1

Consider the set $\mathcal{L}$ of free resource-less states and a resource state $\rho$ with robustness $\mathcal{R}_\mathcal{L} (\rho)$, as defined by Eq. eq:Robustness. The work that can be extracted given access to a thermal bath at inverse temperature $\beta$ satisfies provided that $\lambda \geq \beta^{-1} S(\rho) / \mathcal{R}_\mathcal{L} (\rho)$. Here, $Y^*$ is an optimal robustness witne

Figures (1)

  • Figure 1: This figure illustrates the work-extraction protocol described in Sec. \ref{['sec:examples']}. In Stage 1 (Initial State), the working medium, characterized by a null Hamiltonian, is thermalized at the background bath at inverse temperature $\beta$, while the fuel system contains the resource state $\rho$. The Hamiltonian of the working medium is changed reversibly and isothermally, while maintaining contact with the bath, from $H=0$ to $H=\lambda Y^*$. In Stage 2, the system is isolated from the bath and a global swap operation is performed between the working medium and the fuel; this operation is energy-conserving and therefore incurs no work cost or gain. In Stage 3, contact with the bath is re-established and the working medium rethermalizes at inverse temperature $\beta$. Finally, in Stage 4, the Hamiltonian of the working medium is changed reversibly and isothermally, while remaining in contact with the bath, from $H=\lambda Y^*$ back to $H=0$, thereby restoring the initial configuration and enabling the protocol to be repeated with a fresh fuel state. The protocol outputs more work if the input state is nonclassical than if the input state is resourceless, with a relative advantage that increases with the resource robustness $\mathcal{R}_\mathcal{L} (\rho)$.

Theorems & Definitions (9)

  • Theorem 1: Thermodynamic advantages from non-classicality
  • proof
  • Theorem 2
  • proof
  • Corollary 1: Thermodynamic costs of non-classicality
  • Theorem 3: Thermodynamic costs of non-classical state generation
  • proof
  • Theorem 4: Thermodynamic costs of non-classical channels
  • proof