Optimal observables for (non-)equilibrium quantum metrology from the master equation

TL;DR

This paper presents a method to explicitly construct optimal observables for quantum metrology directly from the master equation, applicable to both equilibrium and non-equilibrium open quantum systems, without solving the master equation explicitly.

Contribution

The authors introduce a general approach to derive the symmetric logarithmic derivative from the master equation, enabling optimal measurement design in complex quantum systems.

Findings

Reproduced the SLD for temperature in quantum Brownian motion.

Constructed the optimal observable for non-equilibrium relaxation rate.

Validated the method's applicability to out-of-equilibrium systems.

Abstract

We demonstrate how observables with optimal sensitivity to environmental properties can be constructed explicitly from the master equation of an open-quantum system. Our approach does not rely on the explicit solution of the master equation. This makes the symmetric logarithmic derivative (SLD), the operator of optimal sensitivity and key quantity in quantum metrology, available to a large class of systems of interest, both in and out-of-equilibrium. We validate our approach by reproducing the SLD for temperature in quantum Brownian motion and demonstrate its versatility by constructing the optimal observable for the non-equilibrium relaxation rate.