Universal Precision Limits in General 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 coupled to environments of arbitrary strength and 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 by both entropy production and this forward-backward asymmetry. For general observables, we prove that their relative fluctuation is always bounded from below by a generalized activity term. These results establish a comprehensive framework for understanding precision limits in broad classes of general open quantum systems.