Quantum metrology in a non-Markovian quantum evolution

TL;DR

This paper investigates quantum metrology in non-Markovian environments, identifying optimal states and control strategies that enhance parameter estimation by manipulating quantum information flow and dynamics.

Contribution

It introduces a method to optimize quantum Fisher information in non-Markovian evolution using control fields, revealing the interplay between QFI, non-Markovianity, and entanglement.

Findings

Optimal metrological states are not maximally entangled but evolve fastest.

Control fields can actively enhance information flow and parameter estimation.

A sharp interplay between QFI, non-Markovianity, and entanglement is demonstrated.

Abstract

The problem of quantum metrology under the context of a particular non-Markovian quantum evolution is explored. We study the dynamics of the quantum Fisher information (QFI) of a composite quantum probe coupled to a Lorentzian environment, for a full variety of different classes of parameters. We are able to find the best metrological state which is not maximally entangled but is the one which evolves fastest. This is shown by evidencing a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting over the probes, we show how the total information flow is actively manipulated by the control such as to enhance the parameter estimation at a given final evolution time. At last, under this controlled scenario, a sharp interplay between the dynamics of QFI, non-Markovianity, and entanglement is revealed within different control schemes.