Introduction to quantum Fisher information

Abstract

The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions parametrized by a function. In physical applications the minimal is the most popular. There is a one-to-one correspondence between Fisher informations (called also monotone metrics) and abstract covariances. The skew information and the chi-square-divergence are treated here as particular cases.

21 pages

References in corpus (5)

• Metric adjusted skew information
• Uncertainty principle with quantum Fisher information
• Asymptotic performance of optimal state estimation in quantum two level system
• A volume inequality for quantum Fisher information and the uncertainty principle
• Quantum covariance, quantum Fisher information and the uncertainty principle

Cited by in corpus (82)

• Quantum Coherence as a Resource
• Quantum Fisher information matrix and multiparameter estimation
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Distributed Quantum Metrology and the Entangling Power of Linear Networks
• Beating Rayleigh's Curse by Imaging Using Phase Information
• Extremal properties of the variance and the quantum Fisher information
• Cohering and de-cohering power of quantum channels
• Thermodynamic length in open quantum systems
• A general framework for quantum macroscopicity in terms of coherence
• Quantum Machine Learning: from physics to software engineering
• Generalizable control for quantum parameter estimation through reinforcement learning
• Canonical Energy is Quantum Fisher Information
• Geometric optimisation of quantum thermodynamic processes
• Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit
• Fundamental precision limit of a Mach-Zehnder interferometric sensor when one of the inputs is the vacuum
• The entropy power inequality for quantum systems
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Multipartite Entanglement at Finite Temperature
• Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields
• Achieving the ultimate quantum timing resolution
• Detecting metrologically useful asymmetry and entanglement by a few local measurements
• On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology
• Extremal quantum states
• Behavior of quantum discord, local quantum uncertainty, and local quantum Fisher information in two-spin-1/2 Heisenberg chain with DM and KSEA interactions
• Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure
• A tight Cramér-Rao bound for joint parameter estimation with a pure two-mode squeezed probe
• Sub-Quantum Fisher Information
• Quantum Radars and Lidars: Concepts, realizations, and perspectives
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Fundamental limits of metrology at thermal equilibrium
• Fisher information as a probe of spacetime structure: Relativistic quantum metrology in (A)dS
• The holographic entropy zoo
• State retrieval beyond Bayes' retrodiction
• Local Quantum Uncertainty in Two-Qubit Separable States: A Case Study
• Taming singularities of the quantum Fisher information
• Enhancing the estimation precision of an unknown phase shift in multipartite Glauber coherent states via skew information correlations and local quantum Fisher information
• Information Geometry of Quantum Resources
• Geometric inequalities from phase space translations
• Multiparameter estimation, lower bound on quantum Fisher information and non-Markovianity witnesses of noisy two-qubit systems
• Quantum Continual Learning Overcoming Catastrophic Forgetting
• On exploring the potential of quantum auto-encoder for learning quantum systems
• Accessible precisions for estimating two conjugate parameters using Gaussian probes
• Quantifying the difference between many-body quantum states
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Quantum Amplitude Estimation in the Presence of Noise
• Quantum Wasserstein distance based on an optimization over separable states
• Monitoring variations of refractive index via Hilbert-Schmidt speed and applying this phenomenon to improve quantum metrology
• Fisher Information of a Black Hole Spacetime
• Measurement disturbance and conservation laws in quantum mechanics
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• Fundamental noisy multiparameter quantum bounds
• RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
• A sufficient Entanglement Criterion Based On Quantum Fisher Information and Variance
• Estimating the Unruh effect via entangled many-body probes
• Smooth Metric Adjusted Skew Information Rates
• Complexity and Time
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Universal adversarial perturbations for multiple classification tasks with quantum classifiers
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
• Maps on positive definite operators preserving the quantum ${\chi }_{\alpha }^2$-divergence
• Phase Estimation of Coherent States with a Noiseless Linear Amplifier
• Characterizing non-deterministic noiseless linear amplifiers at the quantum limit
• Quantum correlations for anonymous metrology
• Dispelling Rayleigh's Curse
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• Jaynes-Cummings atoms coupled to a structured environment: Leakage elimination operators and the Petz recovery maps
• Monotone Riemannian metrics and dynamic structure factor in condensed matter physics
• HEE and HSC for flavors: perturbative structure in open string geometries
• Achieving quantum-limited optical resolution
• Magnetic Field Detection Using a Two-Qubit System Under Noisy Heisenberg Interaction
• Correspondence between causality in flat Minkowski spacetime and entanglement in thermofield-double state: Hessian-geometrical study
• Quantum metrology through spectral measurements in quantum optics
• Estimating time in quantum chaotic systems and black holes
• Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
• Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations
• Information geometry of nonmonotonic quantum natural gradient
• Geometric signature of non-Markovian dynamics
• Intensity-Based Axial Localization at the Quantum Limit
• Completely positive mappings and mean matrices