Quantum metrology in a non-Markovian quantum evolution

Abstract

The problem of quantum metrology in 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 the most rapidly. This is shown by demonstrating a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting on the probes, we show how the total information flow is actively manipulated by the control so as to enhance the parameter estimation at a given final evolution time. Finally, under this controlled scenario, a sharp interplay between the dynamics of QFI, non-Markovianity, and entanglement is revealed within different control schemes.

Optimally controlled quantum discrimination and estimation

“…Quantum discrimination and quantum estimation underlie many applications in quantum information science, including quantum hypothesis testing, quantum detection, and quantum sensing. While quantum control has been employed to improve the precision in quantum estimation [47][48][49][50][51][52][53][54][55][56], the use of quantum control in quantum discrimination remains scarce [57][58][59]. This is so despite the fact that one may expect quantum control to help identify fundamental performance bounds of quantum discrimination, similar to those found for quantum computation [6,60] or derive pulse shapes for improved performance with direct relevance to experiments [8,61].…”

Quantum parameter estimation in a dissipative environment

“…In this sense, the probe and its surrounding environment form an open quantum system [32][33][34], which implies the estimation performance can be severely influenced by the environment. To gain a global view and more physical insight into the quantum * wuw@lzu.edu.cn parameter estimation problem, the estimation scheme should be investigated within the framework of quantum dissipative dynamics and how to degrade the noise's impact should be taken into account [35][36][37][38]. Almost all the existing studies of parameter estimation in a noisy environment restricted their attentions to some exactly solvable situations.…”

Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

“…Nevertheless, the efficiency of the QFI flow to detect the non-Markovianity in various scenarios has not been yet analytically compared with the other faithful witnesses of non-Markovianity (see Ref. 72 for a numerical study on the interplay between the dynamics of the QFI and the trace distance an important indicator of non-Markovianity). On the other hand, the HSS flow has been recently proposed as a faithful witness of non-Markovianity in low dimensional systems 73 , 74 .…”