Thermodynamic work capacity of quantum information processing

TL;DR

This paper introduces a resource-theoretic free energy for quantum channels, quantifying the maximum work extractable during channel transformations and revealing the thermodynamic limits of quantum information processing.

Contribution

It defines the thermodynamic work capacity of quantum channels and establishes its operational meaning in asymptotic athermality distillation and formation.

Findings

The free energy of a quantum channel is proportional to its relative entropy from the thermal channel.

The optimal work in channel conversion equals the difference in free energies.

The resource theory of athermality for quantum channels is asymptotically reversible.

Abstract

We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.