Finite resolution ancilla-assisted measurements of quantum work distributions

TL;DR

This paper proposes a finite resolution, ancilla-assisted measurement protocol for quantum work distributions, analyzing how measurement affects the estimation of work and fluctuation relations in quantum systems.

Contribution

It introduces a measurement model with finite localization and interaction time, providing corrections to fluctuation relations for both commuting and non-commuting Hamiltonians.

Findings

Quantifies measurement effects on work distribution estimates

Derives corrections to Jarzynski and Crooks relations

Analyzes impact of measurement resolution on quantum thermodynamics

Abstract

Work is an observable quantity associated with a process, however there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von-Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation. This measurement model allows us to quantify the effect that measuring has on the estimated work distribution, and associated average work done on the system and average heat exchanged with the measuring apparatus.