Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein's lemma. (19th November 2021)

• Record Type: Journal Article
• Authors: Sagawa, Takahiro; Faist, Philippe; Kato, Kohtaro; Matsumoto, Keiji; Nagaoka, Hiroshi; Brandão, Fernando G S L
• Is Part Of: Journal of physics. Volume 54:Number 49(2021)
• Publication Date: 2021-11-19
• Subjects: quantum information -- quantum thermodynamics -- quantum ergodic theory -- many-body quantum systems -- quantum hypothesis testing; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac333c
• Languages: English
• ISSNs: 1751-8113

Abstract

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 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.