Abstract
We find necessary and sufficient conditions to determine the interconvertibility of quantum systems under time-translation covariant evolution, and use it to solve several problems in quantum thermodynamics both in the single-shot and asymptotic regimes. It is well known that the resource theory of quantum athermality is not reversible, but in Brandão et al. [Phys. Rev. Lett. 111, 250404 (2013)] it was claimed that the theory becomes reversible “provided a sublinear amount of coherent superposition over energy levels is available.” Here we show that if a sublinear amount of coherence among energy levels were considered free, then the resource theory of athermality would become trivial. Instead, we show that by considering a sublinear amount of energy to be free, the theory of athermality becomes reversible for the pure-state case. A proof of the same claim for the mixed-state case is still lacking.
- Received 21 June 2022
- Revised 21 September 2022
- Accepted 7 November 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.040323
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Erratum
Erratum: Role of Quantum Coherence in Thermodynamics [PRX Quantum 3, 040323 (2022)]
Gilad Gour
PRX Quantum 4, 040901 (2023)
Popular Summary
Quantum coherence lies at the heart of many nonintuitive quantum phenomena and is arguably the key ingredient responsible for the second quantum revolution of the 21st century. It also paves the way to the newly emerging field of quantum thermodynamics that aims create a bridge between thermodynamics and quantum mechanics. Yet, despite the enormous efforts, the role of quantum coherence in thermal systems is quite controversial and somewhat vague, even today. Consequently, in recent years a new approach to thermodynamics has been developed that is based on the recognition that systems outside of thermal equilibrium can be viewed as resources that are consumed in certain thermodynamical tasks such as work extraction or cooling. In this paper we use this resource-theoretic approach and introduce a new systematic framework to quantify, distribute, and manipulate quantum coherence in thermodynamical systems.
One of the key features of quantum coherence is that it leads to irreversibility in thermodynamics that does not exists in the classical domain. That is, thermal systems with quantum coherence can be used to extract (classical) thermodynamical work, but the converse process in which a thermal energy battery is used to prepare a system with quantum coherence is not possible by thermal operations alone. In this paper we show that by considering asymptotically negligible resources, reversibility can be restored at least in the pure-state domain. Such a reversibility property is extremely desirable, as quantum coherence is sensitive to noise and reversibility ensures that it is not waisted during thermodynamical processes.