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Physica Scripta

Individual versus simultaneous estimation of two parameters in a correlated noisy environment

You-neng Guo, Xiangjun Chen, Cheng Fu Yang, Qin Xie

Published Sep 22, 2023• 1 citation
Publisher

Abstract

Abstract Recently, the phase parametric estimation for a single qubit system driven by a phase noisy laser under non-Markovian dynamics has been reported. We here generalize the single-parameter estimation to the two-parameter scenario where a two-qubit system is influenced by correlated phase noisy laser, and compare the performances of two-parameter estimation in both individual and simultaneous strategies by using the quantum Fisher information and the quantum Fisher information matrix, respectively.Our results show the phase parametric estimation precision can be improved due to the memory effect arising from successive applications of the noisy laser. With the memory coefficient $\mu$ increasing, the precision of parameter estimation becomes more accuracy. Besides, the phase parameter estimation precision can be well enhanced by engineering the ratios of classical phase noisy laser rate and system-environment coupling strength dependent of Markovian or non-Markovian regions. What's more, we find the simultaneous estimation of two-phase parameters is not always advantageous over the individual strategy.

DOI
10.1088/1402-4896/acfc7d

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The dynamics of quantum Fisher information (QFI) of the phase parameter in a driven two-state system is studied within the framework of the non-Markovian dissipative process. The influences of memory effects, classical driving, and detunings on the parameter-estimation precision are demonstrated by exactly solving the Hamiltonian under rotating-wave approximation. In sharp contrast with the results obtained in the presence of Markovian dissipation, we find that classical driving can drastically enhance the QFI, namely, the precision of parameter estimation in the non-Markovian regime. Moreover, the parameter-estimation precision may even be preserved from the influence of surrounding non-Markovian dissipation with the assistance of classical driving. Remarkably, we reveal that the enhancement and preservation of QFI highly depend on the combination of classical driving and non-Markovian effects. Finally, a phenomenological explanation of the underlying mechanism is presented in detail via the quasimode theory.
In this paper, the dynamics of quantum correlation quantified by local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for two uncoupled qubits driven by classical phase noisy laser have been investigated. The results show that, both LQU and LQFI exhibit similar behaviours, either display exponential decay or oscillatory decay with revivals depending on the ratios of classical phase noisy laser rate and system-environment coupling strength. Beside, our results also confirm the amount of quantum correlation measured by LQU is strictly bounded by LQFI in an open system. Finally, we propose a scheme to protect quantum correlation against classical phase noisy laser with the technique of weak measurement and reversal.
Abstract We analytically investigate the dynamics of quantum Fisher information of two qubits in independent environments for both uncorrelated and entangled input states. Especially, we observe that, in the non-Markovian regime and resonant case, quantum Fisher information of uncorrelated input state vanishes only at discrete time point whereas that of entangled input state can disappear during finite time interval. It shows that quantum Fisher information, which determines the parameter estimation precision, is strongly affected by the environment memory effects, and the advantage of entanglement-enhance metrology no longer exists even for a very short time. We also note that quantum Fisher information for two kinds of input states can be preserved under appropriate qubit-reservoir detuning.