Randomly measured quantum particles and thermal noise

TL;DR

This paper investigates the differences between quantum particles subjected to random measurements and those influenced by random thermal noise, highlighting how nonlinear observables can distinguish these effects.

Contribution

It introduces a comparison between random measurement-induced dynamics and thermal noise effects on quantum particles, emphasizing the role of nonlinear observables.

Findings

Linear observables cannot differentiate measurement from noise

Nonlinear observables reveal measurable distinctions

Explicit calculations of observable expectations

Abstract

We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time, which could also be thought of as (possibly thermal) noise. We calculate expectations of observables both linear and nonlinear in the density matrix. We demonstrate explicitly that while linear observables cannot distinguish between random measurements and random noise, measurable distinctions can be seen in nonlinear observables.