No-go theorem for the characterisation of work fluctuations in coherent quantum systems

TL;DR

This paper proves that no measurement scheme can fully characterize work fluctuations in quantum systems with initial coherence, but a two-copy measurement approach offers partial improvements.

Contribution

It establishes a no-go theorem for work fluctuation characterization in coherent quantum systems and proposes a two-copy measurement scheme as a partial solution.

Findings

No measurement scheme can satisfy all criteria for coherent states.

Collective measurements on multiple copies still cannot fully characterize work fluctuations.

A two-copy measurement scheme enables partial description of coherent transformations.

Abstract

An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement both at the beginning and at the end of the process, the first measurement destroys any initial coherence in the energy basis. Here we seek for extensions of this approach which can possibly account for initially coherent states. We consider all measurement schemes to estimate work and require that (i) the difference of average energy corresponds to average work for closed quantum systems, and that (ii) the work statistics agree with the standard two-measurement scheme for states with no coherence in the energy basis. We first show that such a scheme cannot exist. Next, we consider the possibility of performing collective measurements on several copies of the state and prove that it is still impossible to satisfy simultaneously requirements (i) and (ii). Nevertheless, improvements do appear, and in particular we develop a measurement scheme which acts simultaneously on two copies of the state and allows to describe a whole class of coherent transformations.