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Enhancement of quantum Fisher information by periodic pulse control under Markovian relaxation

Wang, Haowei, Xiaoyun Wang, Dazhi Xu

Published Sep 14, 2026• 0 citations
Publisher
DOI
10.5281/zenodo.22744492

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Communications in Theoretical Physics•Sep 26, 2024•0 citations
The estimation degree of a teleported state using two different quantum channels by means of quantum Fisher information is discussed. It consists of using two different noisy channels generated from an interaction between an open quantum system and its surrounding environment under Davies-Markovian dynamics. However, when small interacted system–environment parameters and a small number of detuning parameters are taken into account, a robust estimation degree is obtained. Moreover, it is possible to estimate various system–environment parameters related to the energy relaxation time and dephasing time. By controlling these parameters, we conclude that maximally entangled channels and robust estimation degrees by means of quantum Fisher information are achieved when the energy relaxation and dephasing times vanish.
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.
Abstract Finding the optimal control is of importance to quantum metrology under a noisy environment. In this paper, we tackle the problem of finding the optimal control to enhance the performance of quantum metrology under an arbitrary non-Markovian bosonic environment. By introducing an equivalent pseudomode model, the non-Markovian dynamic evolution is reduced to a Lindblad master equation, which helps us to calculate the gradient of quantum Fisher information and perform the gradient ascent algorithm to find the optimal control. Our approach is accurate and circumvents the need for the Born–Markovian approximation. As an example, we consider the frequency estimation of a spin with pure dephasing under two types of non-Markovian environments. By maximizing the quantum Fisher information at a fixed evolution time, we obtain the optimal multi-axis control, which results in a notable enhancement in quantum metrology. The advantage of our method lies in its applicability to the arbitrary non-Markovian bosonic environment.