Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Discontinuity and Protection of Quantum Fisher Information for a Two-Qubit System*

Guoyou Wang, Ji-Bing Yuan, Hao‐Sheng Zeng

Published Nov 1, 2015• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/64/5/495

Related papers

Non-Markovian effect on the precision of parameter estimation

K. Berrada

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.

Physical Review A•Sep 10, 2013•108 citations

Optimal quantum parameter estimation of two interacting qubits under decoherence

Qiang Zheng, Yao Yao, Yong Li

We investigate the parameter estimation problem in a two-qubit system, in which each qubit is independently interacting with its Markovian environment. We study in detail the sensitivity of the estimation on the decoherence rate $γ$ and the two-qubit interaction strength $v$. In particular, the dynamics of quantum Fisher information are employed as a measure to quantify the precision of the estimations. We find that the quantum Fisher information with respect to the decoherence rate scales like $t^2/[\exp(γt)-1]$ and $\exp(-2γt)$ in the unitary limit and the completely decoherent limit, respectively. When we estimate the interaction strength $v$, the quantum Fisher information shows oscillation behavior in term of time. In addition, our results provide further evidence that the entanglement of the input state may not enhance quantum metrology.

arXiv:1401.2733•Jan 13, 2014•0 citations

Dynamics of the quantum Fisher information in a spin-boson model

Xiang Hao, Ning-Hua Tong, Shiqun Zhu

The quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information flows from the environments to qubits after a number of times if the bath parameter s is larger than a critical value which is related to temperature. The sudden-change behavior will happen during the evolution of the quantum Fisher information of the maximal entanglement state in the non-Markovian environments. The sudden-change times can be varied with the change of the bath parameter s . For a very large number of entangled qubits, the sudden-change behavior of the maximal quantum Fisher information can be used to characterize the existence of the entanglement. The metrology strategy based on the quantum correlated state leads to a lower phase uncertainty when compared with the uncorrelated product state.

arXiv:1311.5951•Journal of Physics A Mathematical and Theoretical•Aug 8, 2013•14 citations

Dynamical Change of Quantum Fisher Information of Cavity-Reservoir Systems*

Jiang Huang, Qin Xie

Abstract We study the quantum Fisher information (QFI) dynamics of the phase parameter in the enlarged cavity-reservoir systems at zero temperature under two situations of large N limit and non-Markovian environment, respectively. We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution. The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously. Moreover, we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.

Communications in Theoretical Physics•Apr 1, 2016•1 citation

Trapping phenomenon of the parameter estimation in asymptotic quantum states

K. Berrada

Abstract In this paper, we study in detail the behavior of the precision of the parameter estimation in open quantum systems using the quantum Fisher information (QFI). In particular, we study the sensitivity of the estimation on a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, the precision of the estimation can even persist asymptotically for different effects of the initial parameters. We find that the QFI can be resistant to the action of the environment with respect to the initial asymptotic states, and it can persist even in the asymptotic long-time regime. In addition, our results provide further evidence that the initial pure and separable mixed states of the input state may enhance quantum metrology. These features make quantum states in this kind of environment a good candidate for the implementation of different schemes of quantum optics and information with high precision. Finally, we show that this quantity may be proposed to detect the amount of the total quantum information that the whole state contains with respect to projective measurements.

Laser Physics•Jul 21, 2016•0 citations

Quantum metrology with a non-Markovian qubit system

Jiang Huang, Wen-Qing Shi, Yu-Ping Xie +2 more

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.

Chinese Physics B•Dec 1, 2018•0 citations
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.
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-QQQ 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.
We investigate the parameter estimation problem in a two-qubit system, in which each qubit is independently interacting with its Markovian environment. We study in detail the sensitivity of the estimation on the decoherence rate γγγ and the two-qubit interaction strength vvv. In particular, the dynamics of quantum Fisher information are employed as a measure to quantify the precision of the estimations. We find that the quantum Fisher information with respect to the decoherence rate scales like t2/[exp⁡(γt)−1]t^2/[\exp(γt)-1]t2/[exp(γt)−1] and exp⁡(−2γt)\exp(-2γt)exp(−2γt) in the unitary limit and the completely decoherent limit, respectively. When we estimate the interaction strength vvv, the quantum Fisher information shows oscillation behavior in term of time. In addition, our results provide further evidence that the entanglement of the input state may not enhance quantum metrology.
The quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information flows from the environments to qubits after a number of times if the bath parameter s is larger than a critical value which is related to temperature. The sudden-change behavior will happen during the evolution of the quantum Fisher information of the maximal entanglement state in the non-Markovian environments. The sudden-change times can be varied with the change of the bath parameter s . For a very large number of entangled qubits, the sudden-change behavior of the maximal quantum Fisher information can be used to characterize the existence of the entanglement. The metrology strategy based on the quantum correlated state leads to a lower phase uncertainty when compared with the uncorrelated product state.
Abstract We study the quantum Fisher information (QFI) dynamics of the phase parameter in the enlarged cavity-reservoir systems at zero temperature under two situations of large N limit and non-Markovian environment, respectively. We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution. The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously. Moreover, we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.
Abstract In this paper, we study in detail the behavior of the precision of the parameter estimation in open quantum systems using the quantum Fisher information (QFI). In particular, we study the sensitivity of the estimation on a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, the precision of the estimation can even persist asymptotically for different effects of the initial parameters. We find that the QFI can be resistant to the action of the environment with respect to the initial asymptotic states, and it can persist even in the asymptotic long-time regime. In addition, our results provide further evidence that the initial pure and separable mixed states of the input state may enhance quantum metrology. These features make quantum states in this kind of environment a good candidate for the implementation of different schemes of quantum optics and information with high precision. Finally, we show that this quantity may be proposed to detect the amount of the total quantum information that the whole state contains with respect to projective measurements.
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.