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

arXiv:1912.04675 · Physical Review A

Quantum metrology in a non-Markovian quantum evolution

Nicolás Mirkin, Martín Larocca, Diego A. Wisniacki

Published Aug 24, 2020• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.022618

Related papers

Quantum force estimation in arbitrary non-Markovian bath

Camille Lombard Latune, Ilya Sinayskiy, Francesco Petruccione

The force estimation problem in Quantum Metrology with an arbitrary non-Markovian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. We emphasis the effects of the non-Markovian bath by studying the short time behavior and find out the essence of non-Markovian effects such as increase in quantum Fisher information. We show that at this time scale the non-Markovian dynamics is much closer to the free dynamics than the Markovian equivalent. This brings huge consequences for the sequential measurement as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow band.

•Apr 29, 2016•0 citations

Quantum metrology with optimal control under an arbitrary non-Markovian bosonic environment

Likun Zhou, Wen Yang

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.

Communications in Theoretical Physics•Sep 26, 2024•0 citations

Quantum Metrology for Non-Markovian Processes

Anian Altherr, Yuxiang Yang

Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an algorithm that evaluates this quantum Fisher information via semidefinite programming. We apply our framework to noisy frequency estimation, where we find that the optimal performance of quantum metrology is better in the non-Markovian scenario than in the Markovian scenario and explore the possibility of efficient sensing via simple variational circuits.

arXiv:2103.02619•Physical Review Letters•Aug 2, 2021•63 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

Quantum metrology of a structured reservoir

Youssef Aiache, Asghar Ullah, Özgür Esat Müstecaplıoğlu +1 more

Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.

arXiv:2503.16261•Physical Review A•May 28, 2025•5 citations

Quantum Fisher information power of quantum evolutions

Jun‐Long Zhao, Yanhui Zhou, Dong‐Xu Chen +5 more

Abstract Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV = 1.

Journal of Physics A Mathematical and Theoretical•Jun 6, 2024•0 citations
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.
The force estimation problem in Quantum Metrology with an arbitrary non-Markovian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. We emphasis the effects of the non-Markovian bath by studying the short time behavior and find out the essence of non-Markovian effects such as increase in quantum Fisher information. We show that at this time scale the non-Markovian dynamics is much closer to the free dynamics than the Markovian equivalent. This brings huge consequences for the sequential measurement as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow band.
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.
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an algorithm that evaluates this quantum Fisher information via semidefinite programming. We apply our framework to noisy frequency estimation, where we find that the optimal performance of quantum metrology is better in the non-Markovian scenario than in the Markovian scenario and explore the possibility of efficient sensing via simple variational circuits.
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.
Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.
Abstract Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV = 1.