Determining the continuous family of quantum Fisher information from linear-response theory

  title={Determining the continuous family of quantum Fisher information from linear-response theory},
  author={Tomohiro Shitara and Masahito Ueda},
  journal={Physical Review A},
The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher information can be determined from linear response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates the linear response function to generalized covariances and hence allows us to determine the quantum… Expand

Figures and Tables from this paper

Fluctuation-dissipation theorem for non-equilibrium quantum systems
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a systemExpand
Lower bounds on the quantum Fisher information based on the variance and various types of entropies
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to aExpand
Quantum Fisher information matrix and multiparameter estimation
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However,Expand
Quantum response theory for nonequilibrium steady states
We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discussExpand
Coherence-variance uncertainty relation and coherence cost for quantum measurement under conservation laws
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term forExpand
On the relation between the monotone Riemannian metrics on the space of Gibbs thermal states and the linear response theory
The proposed in J. Math. Phys. v.57,071903 (2016) analytical expansion of monotone (contractive) Riemannian metrics (called also quantum Fisher information(s)) in terms of moments of the dynamicalExpand
Out-of-time-order fluctuation-dissipation theorem.
A generalized fluctuation-dissipation theorem is proved for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which are bipartite OTOCs for general quantum systems in thermal equilibrium and it is shown that the theorem can be generalized to higher-order n-partite OT OCs as well as in the form of generalized covariance. Expand
Phase transitions in quantum annealing of an NP-hard problem detected by fidelity susceptibility
Quantum annealing (QA) for the NP-hard maximum independent set problem with a unique solution is studied using the quantum Monte Carlo method. A fraction of the samples exhibit first-order phaseExpand
Strong chaos of fast scrambling yields order: Emergence of decoupled quantum information capsules
Abstract The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems.Expand
Macroscopic quantum states: measures, fragility and implementations
Large-scale quantum effects have always played an important role in the foundations of quantum theory. With recent experimental progress and the aspiration for quantum enhanced applications, theExpand


Quantum information-geometry of dissipative quantum phase transitions.
It is argued that the fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them. Expand
Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
We discuss two quantum analogues of the Fisher information, the symmetric logarithmic derivative Fisher information and Kubo–Mori–Bogoljubov Fisher information from a large deviation viewpoint ofExpand
Multiple-parameter quantum estimation and measurement of nonselfadjoint observables
  • H. Yuen, M. Lax
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1973
It is shown that the optimal receiver measures the photon annihilation operator, which corresponds to optical heterodyning, demonstrating the possible optimality of nonselfadjoint operators and clearly indicates the importance of considering more general quantum measurements in quantum signal detection. Expand
Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity underExpand
Quantum critical scaling of the geometric tensors.
This Letter shows that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. Expand
Heisenberg uncertainty relation for mixed states
The Heisenberg uncertainty relation sets a fundamental limit for quantum measurement of incompatible observables. Its standard form derived by Weyl and Robertson is of purely quantum nature when theExpand
The Bogoliubov inner product in quantum statistics
A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relativeExpand
Wigner–Yanase information on quantum state space: The geometric approach
In the search of appropriate Riemannian metrics on quantum state space, the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics withExpand
Fisher information and multiparticle entanglement
The Fisher information F gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometerExpand
Quantum metrology with nonequilibrium steady states of quantum spin chains
We consider parameter estimations with probes being the boundary driven/dissipated non- equilibrium steady states of XXZ spin 1/2 chains. The parameters to be estimated are the dis- sipation couplingExpand