Can quantum fluctuations be consistently monitored?

TL;DR

This paper investigates the limits of monitoring quantum fluctuations in many-body systems, revealing that while macroscopic averages can be tracked consistently, fluctuations generally cannot, except in specific special cases.

Contribution

It analytically demonstrates the non-monotonic behavior of quantum fluctuations and identifies conditions under which they can be monitored consistently, extending the decoherent histories formalism.

Findings

Fluctuations cannot be generally monitored consistently in quantum systems.

Exceptions occur at infinite temperature, critical points, and in semiclassical regimes.

Susceptibility quantifies the degree of non-consistency in monitoring fluctuations.

Abstract

Recent works on the decoherent histories formalism suggested that macroscopic quantities (extensive sums of local observables) in quantum many-body systems can be consistently monitored: The existence of past measurements does not alter future outcome distribution. Here, we show that fluctuations of macroscopic quantities cannot be consistently monitored in general, in contrast to their intensive mean value. Exceptions include fluctuations at infinite temperature, at critical points, and in semiclassical systems. We analytically quantify non-consistency in terms of susceptibility, and obtain related results on entropy growth under noisy unitary.