Thermodynamic Implementations of Quantum Processes

Abstract

Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. As related results we find a new single-shot implementation of time-covariant processes and conditional erasure with nontrivial Hamiltonians, a new proof of the asymptotic equipartition property of the coherent relative entropy, and an optimal implementation of any i.i.d. process with thermal operations for a fixed i.i.d. input state. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

46+15 pages, 2 figures. The appendix of arXiv:1807.05610 was split off and reworked into this technical companion paper. Version v2 reflects the journal accepted version but is extended with some additional related results (Section 8) that are not included in the published work

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Cited by in corpus (9)

• Reassessing thermodynamic advantage from indefinite causal order
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Reliable Simulation of Quantum Channels: the Error Exponent
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Thermodynamic criteria for signaling in quantum channels
• Strong symmetries in collision models and physical dilations of covariant quantum maps