Joint measurability in nonequilibrium quantum thermodynamics

TL;DR

This paper explores the measurement of quantum work in nonequilibrium thermodynamics, demonstrating that joint measurability of unsharp energy measurements enables accurate work and free energy assessments beyond traditional projective schemes.

Contribution

It introduces a framework for joint measurability of unsharp energy observables, extending quantum work measurement beyond projective schemes and enabling accurate thermodynamic assessments.

Findings

Joint measurability of unsharp measurements allows for accurate work measurement.

A model with unsharp energy measurements is explicitly constructed.

Bounds for visibility ensure joint measurability and correct work estimation.

Abstract

In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point measurement (TPM) schemes. According to a well known no-go theorem, there is no work observable which satisfies both (i) an average work condition and (ii) the TPM statistics for diagonal input states. Such projective measurements represent a restrictive class among all possible measurements. It is desirable, both from a theoretical and experimental point of view, to extend the scheme to the general case including suitably designed unsharp measurements. This shifts the focus to the question what information about work and its fluctuations one is able to extract from such generalized measurements. We show that the no-go theorem no longer holds if the observables in a TPM scheme are jointly measurable for any intermediate unitary evolution. We explicitly construct a model with unsharp energy measurements and derive bounds for the visibility that ensure joint measurability. In such an unsharp scenario a single work measurement apparatus can be constructed that allows us to determine the correct average work and to obtain free energy differences with the help of a Jarzynski equality.