Quantum sensing of open systems: Estimation of damping constants and temperature

TL;DR

This paper establishes quantum precision limits for estimating damping constants and temperature in lossy bosonic channels, highlighting optimal states and measurement strategies for enhanced accuracy in practical sensing applications.

Contribution

It introduces analytic lower bounds for estimation uncertainty using a purification approach and identifies optimal states and measurement protocols for damping and temperature estimation.

Findings

Fock states minimize uncertainty at zero temperature

Boson-counting is optimal for damping estimation

Sequential measurements significantly improve precision

Abstract

We determine quantum precision limits for estimation of damping constants and temperature of lossy bosonic channels. A direct application would be the use of light for estimation of the absorption and the temperature of a transparent slab. Analytic lower bounds are obtained for the uncertainty in the estimation, through a purification procedure that replaces the master equation description by a unitary evolution involving the system and ad hoc environments. For zero temperature, Fock states are shown to lead to the minimal uncertainty in the estimation of damping, with boson-counting being the best measurement procedure. In both damping and temperature estimates, sequential pre-thermalization measurements, through a stream of single bosons, may lead to huge gain in precision.