Quantum work statistics and resource theories: bridging the gap through Renyi divergences

TL;DR

This paper links quantum work statistics with resource theories by expressing the cumulant generating function of work through quantum Renyi divergences, establishing bounds, and exploring an extended framework with a control switch and battery.

Contribution

It introduces a novel connection between quantum work statistics and resource theories using Renyi divergences, providing bounds and an extended framework for work reconstruction.

Findings

Cumulant generating function of work recast as quantum Renyi divergences

Derived bounds for the first moment of work using convexity

Extended framework with control switch and auxiliary battery

Abstract

The work performed on or extracted from a non-autonomous quantum system described by means of a two-point projective-measurement approach takes the form of a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Renyi divergences, and by exploiting convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches on the one hand and resource theories for quantum thermodynamics on the other hand, a theory in which Renyi divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstruct the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource theoretic settings.