Response Kinetic Uncertainty Relation for Markovian Open Quantum System

TL;DR

This paper extends the response kinetic uncertainty relation to open quantum systems described by Lindblad equations, linking measurement precision, system response, and quantum effects through the quantum Cramér-Rao bound.

Contribution

It generalizes the classical response KUR to quantum systems using the quantum Cramér-Rao bound, revealing bounds on measurement precision and system sensitivity in open quantum dynamics.

Findings

Bound on observable precision using quantum Cramér-Rao inequality

Conditions where quantum activity and transition terms vanish

Verification in a two-level atom model

Abstract

The thermodynamics and kinetics of a nonequilibrium classical system fundamentally constrain the precision of an observable regarding the celebrated thermodynamic uncertainty relation (TUR) and the kinetic uncertainty relation (KUR). They have been extended to open quantum systems obeying the Lindblad master equation where unique quantum effects are identified. Recently, a new set of principles that further incorporate the response of a classical system to an external perturbation have been discovered, named the response TUR and the response KUR (R-KUR). In this work, we generalize the classical R-KUR using the quantum Cram\'er-Rao bound to the steady state of the Lindblad master equation. The precision and the sensitivity of a measured observable are bounded from above by the conventional quantum dynamical activity and a perturbation-induced inter-subspace transition term. We provide sufficient conditions such that either of the two contributions vanishes, implying their equal importance. We verify our result and illustrate the conditions in an exactly solvable two-level atom.