A single measurement scheme for quantum work statistics based on coherent or squeezing state

TL;DR

This paper introduces a unified measurement scheme using coherent or squeezing states as apparatus to analyze quantum work statistics, explicitly incorporating initial quantum coherence and connecting to traditional energy measurement results.

Contribution

It proposes a novel framework for quantum work measurement with harmonic oscillators, explicitly accounting for initial coherence and linking to standard schemes.

Findings

Work is proportional to the change in the real part of the coherent state parameter.

Work distribution includes initial quantum coherence effects.

Quantum coherence significantly affects work statistics when driving velocity matches system transition frequency.

Abstract

In order to investigate the role of initial quantum coherence in work probability distribution, it is necessary to explicitly consider a concrete measurement apparatus to record work rather than implicitly appealing to perform an energy measurement. In this paper, we consider a harmonic oscillator with coherent or squeezing state as measurement apparatus, and propose a unified framework of quantum work statistics for arbitrary initial state. We find that work is proportional to the change of the real part of coherent state parameter, i.e., quantum work can be estimated by the coherent state parameter. The resulting work probability distribution includes the initial quantum coherence, and can be reduced to result of traditional two projective energy measurement scheme (TPM) by squeezing the state of the harmonic oscillator. As an application, we consider a driven two-level system and investigate the effects of driving velocity on work statistics. We find that only when the driving velocity matches the transition frequency of the system can initial quantum coherence play an important role.