Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma

Abstract

For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback-Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein's lemma for quantum hypothesis testing beyond independent and identically distributed (i.i.d.) situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

59 pages. See short companion paper Phys. Rev. Lett. 123, 250601

References in corpus (12)

• Reference frames, superselection rules, and quantum information
• Coding Theorem and Strong Converse for Quantum Channels
• Quantum coherence, time-translation symmetry and thermodynamics
• Leftover Hashing Against Quantum Side Information
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Large deviations in quantum lattice systems: one-phase region
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Reverse Test and Characterization of Quantum Relative Entropy
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Thermodynamic Implementations of Quantum Processes

Cited by in corpus (4)

• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• An information-theoretic treatment of quantum dichotomies
• The $d$-Majorization Polytope
• Reachability in Controlled Markovian Quantum Systems: An Operator-Theoretic Approach