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

Physical Review A

Dynamics of quantum Fisher information from a time-local non-Markovian master equation with decoherence rates and operators depending on the estimated parameter

Mihaela Vatasescu

Published Oct 10, 2022• 3 citations
Publisher

Abstract

We analyze the dynamics of the quantum Fisher information (QFI) in the case of a two-dimensional open quantum system obeying a time-local non-Markovian master equation in the canonical form, characterized by canonical decoherence rates and operators that depend on the parameter to be estimated. This last condition brings a framework in which the information about the parameter is structurally encoded not only in the open system, but also in the system-environment interaction or/and correlations, and in some environment properties. We derive analytical formulas for the decompositions of the QFI flow and of the purity dynamics in terms associated to the canonical decoherence rates. In contrast to the results presented in X.-M. Lu et al. [Phys. Rev. A 82, 042103 (2010)], we show that, in this extended framework, the QFI flow contains not only the subflows corresponding to the decoherence rates, but also supplementary terms which originate in the state dependence on the estimated parameter; moreover, the signs of the QFI subflows associated to the decoherence rates are not correlated to the signs of the rates. We show that a pertinent connection between the QFI flow and non-Markovianity can be realized using the canonical measures defined from the negative canonical decoherence rates. We employ this theoretical framework to explore the QFI flow and its subflows in two cases of quantum evolutions directed by master equations with decoherence rates or/and operators depending on the estimated parameter: (i) the Markovian nonunital time evolution of a qubit under the generalized amplitude damping channel; (ii) the non-Markovian time evolution of a two-dimensional electronic subsystem entangled with its vibrational environment in a molecule.

DOI
10.1103/physreva.106.042204

Related papers

Comment on "Quantum Fisher information flow and non-Markovian processes of open systems"

Mihaela Vatasescu

In [Phys. Rev. A 82, 042103 (2010)], the authors showed that "for a class of the non-Markovian master equations in time-local forms", the quantum Fisher information (QFI) flow can be decomposed into additive subflows corresponding to different dissipative channels. However, the paper does not specify the class of non-Markovian time-local master equations for which their analytic decomposition of the QFI flow is valid. Here we show that several suppositions have to be made in order to reach the central result of Ref. \cite{luwsun10}, which appears to be valid for a narrow class of density operators $ρ(θ;t)$ and quantum Fisher information $\mathcal{F}(θ;t)$, and under strict conditions on the time-local master equation. More precisely, the decomposition of the QFI flow obtained in Ref. \cite{luwsun10} is valid under two conditions not mentioned in the paper: (i) $\frac{d}{dt} \left( \frac{\partial ρ}{\partial θ} \right)=$ $\frac{\partial}{\partial θ} \left( \frac{d ρ}{dt} \right)$; (ii) $\frac{\partial H}{\partial θ}=0$, $\frac{\partial γ_i}{\partial θ}=0$, $\frac{\partial A_i}{\partial θ}=0$, meaning that the Hamiltonian $H(t)$, the decay rates $γ_i(t)$, and the Lindblad operators $A_i(t)$ appearing in the non-Markovian time-local master equation have to not depend on the parameter $θ$ about which the quantum Fisher information is defined.

arXiv:2012.10767•Dec 19, 2020•0 citations

Modulating quantum Fisher information of qubit in dissipative cavity by coupling strength

Danping Lin, Yu Liu, Hong-Mei Zou

By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.

arXiv:1905.06608•Chinese Physics B•Nov 1, 2018•5 citations

Quantum fisher information transfer and distribution in a hierarchical environment

You-neng Guo, Qinglong Tian

How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.

Results in Physics•Sep 1, 2025•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

Nonlocal effects via Local Quantum Fisher Information: Characterizations and Interpretations

R. Muthuganesan

We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing

quant-pharXiv:2606.29795•Physica Scripta•Jun 30, 2026•0 citations

Non-Markovian dynamics of the electronic subsystem in a laser-driven molecule: Characterization and connections with electronic-vibrational entanglement and electronic coherence

Mihaela Vatasescu

Non-Markovian quantum evolution of the electronic subsystem in a laser-driven molecule is characterized through the appearance of negative decoherence rates in the canonical form of the electronic master equation. For a driven molecular system described in a bipartite Hilbert space $\mathcal{H}={\mathcal{H}}_{el}⨂{\mathcal{H}}_{\mathrm{vib}}$ of dimension $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$, we derive the canonical form of the electronic master equation, deducing the canonical measures of non-Markovianity and the Bloch volume of accessible states. We find that one of the decoherence rates is always negative, accounting for the inherent non-Markovian character of the electronic evolution in the vibrational environment. Enhanced non-Markovian behavior, characterized by two negative decoherence rates, appears if there is a coupling between the electronic states $g,\phantom{\rule{0.16em}{0ex}}e$, such that the evolution of the electronic populations obeys $d({P}_{g}{P}_{e})/dt>0$. Non-Markovianity of the electronic evolution is analyzed in relation to temporal behaviors of the electronic-vibrational entanglement and electronic coherence, showing that enhanced non-Markovian behavior accompanies entanglement increase. Taking as an example the coupling of two electronic states by a laser pulse in the ${\mathrm{Cs}}_{2}$ molecule, we analyze non-Markovian dynamics under laser pulses of various strengths, finding that the weaker pulse stimulates the bigger amount of non-Markovianity. Our results show that increase of the electronic-vibrational entanglement over a time interval is correlated to the growth of the total amount of non-Markovianity calculated over the same interval using canonical measures and connected with the increase of the Bloch volume. After the pulse, non-Markovian behavior is correlated to electronic coherence, such that vibrational motion in the electronic potentials which diminishes the nuclear overlap, implicitly increasing the linear entropy of entanglement, brings a memory character to dynamics.

arXiv:1811.08220•Physical Review A•Nov 19, 2018•3 citations
We analyze the dynamics of the quantum Fisher information (QFI) in the case of a two-dimensional open quantum system obeying a time-local non-Markovian master equation in the canonical form, characterized by canonical decoherence rates and operators that depend on the parameter to be estimated. This last condition brings a framework in which the information about the parameter is structurally encoded not only in the open system, but also in the system-environment interaction or/and correlations, and in some environment properties. We derive analytical formulas for the decompositions of the QFI flow and of the purity dynamics in terms associated to the canonical decoherence rates. In contrast to the results presented in X.-M. Lu et al. [Phys. Rev. A 82, 042103 (2010)], we show that, in this extended framework, the QFI flow contains not only the subflows corresponding to the decoherence rates, but also supplementary terms which originate in the state dependence on the estimated parameter; moreover, the signs of the QFI subflows associated to the decoherence rates are not correlated to the signs of the rates. We show that a pertinent connection between the QFI flow and non-Markovianity can be realized using the canonical measures defined from the negative canonical decoherence rates. We employ this theoretical framework to explore the QFI flow and its subflows in two cases of quantum evolutions directed by master equations with decoherence rates or/and operators depending on the estimated parameter: (i) the Markovian nonunital time evolution of a qubit under the generalized amplitude damping channel; (ii) the non-Markovian time evolution of a two-dimensional electronic subsystem entangled with its vibrational environment in a molecule.
In [Phys. Rev. A 82, 042103 (2010)], the authors showed that "for a class of the non-Markovian master equations in time-local forms", the quantum Fisher information (QFI) flow can be decomposed into additive subflows corresponding to different dissipative channels. However, the paper does not specify the class of non-Markovian time-local master equations for which their analytic decomposition of the QFI flow is valid. Here we show that several suppositions have to be made in order to reach the central result of Ref. \cite{luwsun10}, which appears to be valid for a narrow class of density operators ρ(θ;t)ρ(θ;t)ρ(θ;t) and quantum Fisher information F(θ;t)\mathcal{F}(θ;t)F(θ;t), and under strict conditions on the time-local master equation. More precisely, the decomposition of the QFI flow obtained in Ref. \cite{luwsun10} is valid under two conditions not mentioned in the paper: (i) ddt(∂ρ∂θ)=\frac{d}{dt} \left( \frac{\partial ρ}{\partial θ} \right)=dtd​(∂θ∂ρ​)= ∂∂θ(dρdt)\frac{\partial}{\partial θ} \left( \frac{d ρ}{dt} \right)∂θ∂​(dtdρ​); (ii) ∂H∂θ=0\frac{\partial H}{\partial θ}=0∂θ∂H​=0, ∂γi∂θ=0\frac{\partial γ_i}{\partial θ}=0∂θ∂γi​​=0, ∂Ai∂θ=0\frac{\partial A_i}{\partial θ}=0∂θ∂Ai​​=0, meaning that the Hamiltonian H(t)H(t)H(t), the decay rates γi(t)γ_i(t)γi​(t), and the Lindblad operators Ai(t)A_i(t)Ai​(t) appearing in the non-Markovian time-local master equation have to not depend on the parameter θθθ about which the quantum Fisher information is defined.
By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.
How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.
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.
We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing
Non-Markovian quantum evolution of the electronic subsystem in a laser-driven molecule is characterized through the appearance of negative decoherence rates in the canonical form of the electronic master equation. For a driven molecular system described in a bipartite Hilbert space H=Hel⨂Hvib\mathcal{H}={\mathcal{H}}_{el}⨂{\mathcal{H}}_{\mathrm{vib}}H=Hel​⨂Hvib​ of dimension $2\ifmmode\times\else\texttimes\fi{}{N}_{v}$, we derive the canonical form of the electronic master equation, deducing the canonical measures of non-Markovianity and the Bloch volume of accessible states. We find that one of the decoherence rates is always negative, accounting for the inherent non-Markovian character of the electronic evolution in the vibrational environment. Enhanced non-Markovian behavior, characterized by two negative decoherence rates, appears if there is a coupling between the electronic states g,eg,\phantom{\rule{0.16em}{0ex}}eg,e, such that the evolution of the electronic populations obeys d(PgPe)/dt>0d({P}_{g}{P}_{e})/dt>0d(Pg​Pe​)/dt>0. Non-Markovianity of the electronic evolution is analyzed in relation to temporal behaviors of the electronic-vibrational entanglement and electronic coherence, showing that enhanced non-Markovian behavior accompanies entanglement increase. Taking as an example the coupling of two electronic states by a laser pulse in the Cs2{\mathrm{Cs}}_{2}Cs2​ molecule, we analyze non-Markovian dynamics under laser pulses of various strengths, finding that the weaker pulse stimulates the bigger amount of non-Markovianity. Our results show that increase of the electronic-vibrational entanglement over a time interval is correlated to the growth of the total amount of non-Markovianity calculated over the same interval using canonical measures and connected with the increase of the Bloch volume. After the pulse, non-Markovian behavior is correlated to electronic coherence, such that vibrational motion in the electronic potentials which diminishes the nuclear overlap, implicitly increasing the linear entropy of entanglement, brings a memory character to dynamics.