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

Fisher information in a quantum-critical environment

Zhe Sun, Jian Ma, Xiao-Ming Lu, Xiaoguang Wang

Published Aug 6, 2010• 112 citations
Publisher

Abstract

We consider a process of parameter estimation in a spin-$j$ system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.

DOI
10.1103/physreva.82.022306

Related papers

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

Probing quantum critical points by Fisher information at finite temperature

Qian Wang, Wen-ge Wang

We study the quantum Fisher information (QFI) of a one-dimensional anisotropic XY chain in a transverse field with three-spin interaction. It is shown that the QFI, computed at a finite temperature, can be used to estimate the critical point (CP) of the quantum phase transition (QPT) at zero temperature. The accuracy of the obtained result depends on both the anisotropy parameter of the chain and the local observable used in the computation of QFI.

Modern Physics Letters B•Apr 6, 2017•6 citations

Critical properties of quantum Fisher information of SU(1,1)-dynamic systems

Yuyang Tang, Yu Yang, Min An +4 more

Quantum Fisher information (QFI) may exhibit the irregular behavior at the critical point of phase transitions of a physical system and be very sensitive to slight variations of some controlling parameters. This parameter sensitivity may be used for quantum parameter estimation or quantum sensing. In this study, taking the quantum Rabi model as an example, we investigate the critical properties of the QFI for the parameter estimation at the critical point of the SU(1,1) dynamic systems. We show that the QFI goes divergently in the sixth power law $({T}^{6})$ of the parameter coding time around the critical point. After taking into the consumption of energy during the dynamic evolution, we find that the variation of the QFI around the critical point is scaled by the Heisenberg scaling ${T}^{2}$. It is noticed that for nonclassical initial probe states the scaling of QFI can beat the standard quantum limit $({n}_{0})$ as a function of the initial mean phonon number ${n}_{0}$. The homodyne and phonon-number measurement schemes are compared. We find that the quantum Cram\'er-Rao bound can be reached by use of the phonon-number detection scheme. However, it is more sensitive to the noise than the homodyne detection scheme. We extend the investigation to a two-mode non-Hermitian system and show that the QFI exhibits the same irregular properties at the exceptional point, revealing that for the SU(1,1) dynamic systems the QFI universally diverges as ${T}^{6}$ at the critical point.

Physical Review A•Aug 13, 2024•2 citations

Quantum speed limit and a signal of quantum criticality

Yong-Bo Wei, Jian Zou, Zhao-Ming Wang +1 more

We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.

Scientific Reports•Jan 19, 2016•42 citations

Distinct Critical Scaling of Quantum Fisher Information in a Quantum Rabi Triangle System

Yuyang Tang, Yu Yang, Min An +1 more

Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.

quant-pharXiv:2511.01314•Nov 4, 2025•0 citations

Dynamics of quantum coherence and quantum Fisher information after a sudden quench

Rouhollah Jafari, Alireza Akbari

The dynamics of relative entropy and ${l}_{1}$ norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional $XY$ spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the ${l}_{1}$ norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.

arXiv:2002.00230•Physical Review A•Jun 8, 2020•44 citations
We consider a process of parameter estimation in a spin-jjj system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.
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.
Quantum Fisher information (QFI) may exhibit the irregular behavior at the critical point of phase transitions of a physical system and be very sensitive to slight variations of some controlling parameters. This parameter sensitivity may be used for quantum parameter estimation or quantum sensing. In this study, taking the quantum Rabi model as an example, we investigate the critical properties of the QFI for the parameter estimation at the critical point of the SU(1,1) dynamic systems. We show that the QFI goes divergently in the sixth power law (T6)({T}^{6})(T6) of the parameter coding time around the critical point. After taking into the consumption of energy during the dynamic evolution, we find that the variation of the QFI around the critical point is scaled by the Heisenberg scaling T2{T}^{2}T2. It is noticed that for nonclassical initial probe states the scaling of QFI can beat the standard quantum limit (n0)({n}_{0})(n0​) as a function of the initial mean phonon number n0{n}_{0}n0​. The homodyne and phonon-number measurement schemes are compared. We find that the quantum Cram\'er-Rao bound can be reached by use of the phonon-number detection scheme. However, it is more sensitive to the noise than the homodyne detection scheme. We extend the investigation to a two-mode non-Hermitian system and show that the QFI exhibits the same irregular properties at the exceptional point, revealing that for the SU(1,1) dynamic systems the QFI universally diverges as T6{T}^{6}T6 at the critical point.
We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.
The dynamics of relative entropy and l1{l}_{1}l1​ norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional XYXYXY spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the l1{l}_{1}l1​ norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.