# Universal Precision Limits in General Open Quantum Systems

## TL;DR

This paper establishes universal bounds on the precision of observables in open quantum systems, extending thermodynamic uncertainty relations to non-Markovian regimes with arbitrary environment coupling.

## Contribution

It introduces a generalized framework for precision limits in open quantum systems, incorporating asymmetry and environmental activity beyond Markovian assumptions.

## Key findings

- Relative fluctuation of time-antisymmetric currents is constrained by entropy production and asymmetry.
- Bound on observable fluctuations includes a generalized environmental activity term.
- Framework applies to broad class of non-Markovian open quantum systems.

## Abstract

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian systems, corresponding constraints in the non-Markovian regime remain largely unexplored. In this Letter, we derive universal bounds on the precision of generic observables in open quantum systems that interact with their environments at arbitrary coupling strengths and are subjected to two-point measurements. By introducing an asymmetry term that quantifies the disparity between forward and backward processes, we show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.

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Source: https://tomesphere.com/paper/2508.21567