Saturation of repeated quantum measurements

TL;DR

This paper investigates the limits of information gain in repeated quantum measurements, showing that some measurements saturate while others, like unsharp two-outcome observables, do not, with implications for noise correction.

Contribution

It demonstrates that repeated measurements of unsharp observables never saturate and characterizes the limiting observable, revealing new insights into quantum measurement processes.

Findings

Repeated measurements of certain observables saturate after finite steps.

Repeated L"uders measurements of unsharp observables do not saturate.

Repeated measurements can correct noise in unsharp observables.

Abstract

We study sequential measurement scenarios where the system is repeatedly subjected to the same measurement process. We first provide examples of such repeated measurements where further repetitions of the measurement do not increase our knowledge on the system after some finite number of measurement steps. We also prove, however, that repeating the L\"uders measurement of an unsharp two-outcome observable never saturates in this sense, and we characterize the observable measured in the limit of infinitely many repetitions. Our result implies that a repeated measurement can be used to correct the inherent noise of an unsharp observable.