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Physical Review A

Non-Markovian effect on the precision of parameter estimation

K. Berrada

Published Sep 10, 2013• 108 citations
Publisher

Abstract

We study the non-Markovian effect on the dynamics of the quantum Fisher information (QFI) by exactly solving a model consisting of a qubit system subjects to a zero-temperature reservoir for two different non-Markovian conditions: a high-$Q$ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap, respectively. The phenomenon that the QFI, namely, the precision of estimation, changes dramatically with the environment structure and is affected by the environment memory effects. We find that revivals and retardation of QFI loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial QFI trapping occurs in nonideal photonic band gaps and the decreasing gap width seriously destroys coherence, thus reducing the precision of estimation. These features make the qubit system in non-Markovian environments a good candidate for implementation of quantum optics schemes and information with high precision.

DOI
10.1103/physreva.88.035806

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This manuscript investigates the enhancement of parameter-estimation precision (P-EP) in photonic systems subjected to pure dephasing within Markovian and non-Markovian environments. We employ the quantum Fisher information (QFI) to quantify precision and analyze its dynamics in a system where a single photon's polarization interacts with a structured frequency environment. This environment is engineered using a Fabry-Pérot cavity and characterized by parameters such as the tilt angle, spectral width, and refractive index difference. Our results demonstrate that for specific configurations, particularly at certain angles, the system exhibits pronounced non-Markovian behavior, leading to oscillatory revivals in QFI, which signify periods of enhanced P-EP. Furthermore, we find that narrower spectral widths and smaller refractive index differences amplify these effects, prolonging periods of high QFI and improving estimation precision. These findings are corroborated by von Neumann entropy analysis, which reveals corresponding oscillations in quantum purity. Our study highlights the potential of engineered environments to improve the precision of quantum measurements despite environmental interactions, offering a promising strategy for advancing quantum technologies.
The dynamics of the quantum Fisher information (QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.