Upper Bounds on Fluctuation Growths of Observables in Open Quantum Systems

TL;DR

This paper investigates upper bounds on the rate of fluctuation growth of observables in open quantum systems, extending previous work on closed systems and analyzing how different modeling approaches affect these bounds.

Contribution

It introduces methods to derive fluctuation growth bounds in open quantum systems using Taylor and Dyson series, comparing these to bounds in closed systems.

Findings

Including detailed system and state dynamics yields looser fluctuation bounds.

Derived upper bounds for fluctuation growth in two different open system models.

Compared bounds between open and closed systems to understand the impact of system details.

Abstract

The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed quantum system is upper bounded by the fluctuation of its corresponding velocity-like observable. That bound also indicated a tradeoff between the time derivatives of the mean and the standard deviation. In this paper we will look at open quantum systems in two cases. For the first case we find the generator of evolution for an open system employing both the Taylor expansion and the standard time-ordered evolution via the Dyson series, while in the second case we consider no specific information about the evolution of the system. We then find the rate of fluctuation growth in each case. Comparing the upper bounds for each case and considering the upper bound found for a closed system suggest that including more details by separating the contributions of the system and state dynamics seems to result in looser bounds for the rate of fluctuation growth.