Coherence-enhanced single-qubit thermometry out of equilibrium

TL;DR

This paper demonstrates that quantum coherence in a finite-dimensional quantum thermometer enhances its sensitivity in nonequilibrium thermalization, with maximum sensitivity occurring at finite times during transient dynamics.

Contribution

It analytically proves that initial quantum coherence improves thermometric sensitivity and identifies optimal measurement times during transient thermalization.

Findings

Quantum coherence enhances thermometer sensitivity.

Maximum sensitivity occurs at finite times during transient dynamics.

Finite-time sensitivity can surpass asymptotic limits.

Abstract

The metrological limits of thermometry operated in nonequilibrium dynamical regimes are analyzed. We consider a finite-dimensional quantum system, employed as a quantum thermometer, in contact with a thermal bath inducing Markovian thermalization dynamics. The quantum thermometer is initialized in a generic quantum state, possibly including quantum coherence w.r.t. the Hamiltonian basis. We prove that the sensitivity of the thermometer, quantified by the quantum Fisher information, is enhanced by the quantum coherence in its initial state. We analytically show this in the specific case of qubit thermometers for which the maximization of the quantum Fisher information occurs at a finite time during the transient of the thermalization dynamics. Such a finite-time sensitivity enhancement can be better than the sensitivity that is achieved asymptotically.