A Geometric Perspective on Quantum Parameter Estimation
arXiv:1907.06628 · doi:10.1116/1.5119961
Abstract
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
arXiv comment36 pages, 9 figures
References in corpus (205)
- The Quantum Internet
- Advances in Quantum Metrology
- Gaussian Quantum Information
- Quantum metrology
- Entanglement detection
- Satellite-to-ground quantum key distribution
- Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat The Diffraction Limit
- General Benchmarks for Quantum Repeaters
- Fundamental Limits of Repeaterless Quantum Communications
- Quantum Error Correction for Quantum Memories
- Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
- Field test of quantum key distribution in the Tokyo QKD Network
- The Role of Relative Entropy in Quantum Information Theory
- On the Improvement of Frequency Stardards with Quantum Entanglement
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Quantum metrology from a quantum information science perspective
- Super-resolving phase measurements with a multi-photon entangled state
- Advances in Photonic Quantum Sensing
- Continuous variable quantum information: Gaussian states and beyond
- The elusive Heisenberg limit in quantum enhanced metrology
- A quantum network of clocks
- Quantum Error Correction for Beginners
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Quantum Metrology in Non-Markovian Environments
- Entanglement-free Heisenberg-limited phase estimation
- Fisher information and multiparticle entanglement
- Biological measurement beyond the quantum limit
- Multipartite entanglement and high precision metrology
- De Broglie Wavelength of a Nonlocal Four-Photon
- Quantum metrology with entangled coherent states
- Squeezing as an irreducible resource
- Optimal Quantum Phase Estimation
- Creation of Entanglement by Interaction with a Common Heat Bath
- A Quantum Rosetta Stone for Interferometry
- Quantum enhanced measurements without entanglement
- Quantum State Discrimination
- Generalized Limits for Single-Parameter Quantum Estimation
- Environment Induced Entanglement in Markovian Dissipative Dynamics
- Quantum Enhanced Multiple Phase Estimation
- Using entanglement against noise in quantum metrology
- Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
- Capacities of Quantum Erasure Channels
- Quantum Error Correction: An Introductory Guide
- Ancilla-assisted quantum process tomography
- Quantum phase estimation with lossy interferometers
- Adaptive homodyne measurement of optical phase
- Multi-parameter estimation in networked quantum sensors
- Magnetic field imaging with NV ensembles
- Improved quantum metrology using quantum error-correction
- Compatibility in Multiparameter Quantum Metrology
- The creation of large photon-number path entanglement conditioned on photodetection
- Statistical distinguishability between unitary operations
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Stronger uncertainty relations for the sum of variances
- Using entanglement improves precision of quantum measurements
- Quantum Error Correction for Metrology
- State estimation for large ensembles
- Quantum fidelity for arbitrary Gaussian states
- Experimental quantum-enhanced estimation of a lossy phase shift
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
- All non-classical correlations can be activated into distillable entanglement
- Quantum enhanced estimation of a multi-dimensional field
- General optimality of the Heisenberg limit for quantum metrology
- Topological quantum computing with a very noisy network and local error rates approaching one percent
- Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement
- Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
- Distributed Quantum Metrology and the Entangling Power of Linear Networks
- Optimal quantum estimation of loss in bosonic channels
- Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state
- Fundamental Quantum Limit to Waveform Estimation
- A new approach to the Cramer-Rao type bound of the pure state model
- Deterministic entanglement of photons in two superconducting microwave resonators
- Magnet field sensing beyond the standard quantum limit under the effect of decoherence
- Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
- Fisher information in quantum statistics
- Noisy metrology beyond the standard quantum limit
- Increasing sensing resolution with error correction
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Behavior of Quantum Correlations under Local Noise
- Exponentially Enhanced Quantum Metrology
- Quantum metrology for a general Hamiltonian parameter
- Optimal and Secure Measurement Protocols for Quantum Sensor Networks
- Entanglement-enhanced probing of a delicate material system
- Efficient tools for quantum metrology with uncorrelated noise
- Quantum metrology enhanced by repetitive quantum error correction
- Memory effects in quantum channel discrimination
- Quantum Fisher information for states in exponential form
- Extremal properties of the variance and the quantum Fisher information
- Autonomous Quantum Error Correction and Application to Quantum Sensing with Trapped Ions
- The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
- Uhlmann fidelity between two-mode Gaussian states
- Optimal estimation of joint parameters in phase space
- Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
- Quantum Metrological Limits via a Variational Approach
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- Adaptive quantum metrology under general Markovian noise
- Quantum Hamiltonian identification from measurement time traces
- Phase estimation without a priori knowledge in the presence of loss
- Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
- The Perfect Distinguishability of Quantum Operations
- Discontinuities of the quantum Fisher information and the Bures metric
- Quantum metrology with full and fast quantum control
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Local asymptotic normality for finite dimensional quantum systems
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- Fundamental limits to quantum channel discrimination
- Universal time scaling for Hamiltonian parameter estimation
- Quantum local asymptotic normality based on a new quantum likelihood ratio
- Attaining the ultimate precision limit in quantum state estimation
- Ultimate sensitivity of precision measurements with Gaussian quantum light : a multi-modal approach
- Generation of Large Number-Path Entanglement Using Linear Optics and Feed-Forward
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
- Simple expression for the quantum Fisher information matrix
- Nonlinear quantum metrology of many-body open systems
- Ultimate Precision of Adaptive Noise Estimation
- Estimation of Gaussian quantum states
- Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum
- Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
- Bayesian quantum frequency estimation in presence of collective dephasing
- Quantum metrology for non-linear phase shifts with entangled coherent states
- Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
- Permutation-invariant quantum codes
- Creation of maximally entangled photon-number states using optical fiber multiports
- Flexible resources for quantum metrology
- Optimal full estimation of qubit mixed states
- Ancilla-free quantum error correction codes for quantum metrology
- Local asymptotic normality for qubit states
- Quantum-enhanced metrology for multiple phase estimation with noise
- Optimal measurements for quantum multiparameter estimation with general states
- Local versus Global Strategies in Multi-parameter Estimation
- Random bosonic states for robust quantum metrology
- The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
- Adaptive Quantum Measurements of a Continuously Varying Phase
- Ultimate limits to quantum metrology and the meaning of the Heisenberg limit
- Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology
- Universality of the Heisenberg limit for estimates of random phase shifts
- Entanglement-assisted quantum metrology
- Bounds on Quantum Multiple-Parameter Estimation with Gaussian State
- Entanglement-enhanced quantum metrology in a noisy environment
- Explicit formula for the Holevo bound for two-parameter qubit estimation problem
- Wigner-Yanase skew information as tests for quantum entanglement
- Experimental Demonstration of Adaptive Quantum State Estimation
- Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
- Estimation of unitary quantum operations
- Quantum metrology in the presence of limited data
- Subdiffraction-limited quantum imaging within a living cell
- Quantum multiparameter metrology with generalized entangled coherent state
- Quantum limits to optical point-source localization
- Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge
- Detection of Macroscopic Entanglement by Correlation of Local Observables
- Macroscopic singlet states for gradient magnetometry
- Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
- Quantum metrology for the Ising Hamiltonian with transverse magnetic field
- Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection
- Quantum Fisher information and symmetric logarithmic derivative via anti-commutators
- Quantum multi-parameter estimation with generalized balanced multi-mode NOON-like states
- Optimal estimation of one parameter quantum channels
- Spatial noise filtering through error correction for quantum sensing
- Quantum variance: a measure of quantum coherence and quantum correlations for many-body systems
- Optimal estimation of multiple phases
- Entanglement is not very useful for estimating multiple phases
- Ultimate precision of joint quadrature parameter estimation with a Gaussian probe
- Information Geometry of Complex Hamiltonians and Exceptional Points
- Quantum estimation of a two-phase spin rotation
- Practical quantum metrology with large precision gains in the low photon number regime
- Quantum metrology: Heisenberg limit with bound entanglement
- The role of entanglement in calibrating optical quantum gyroscopes
- Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer
- Feedback control in quantum optics: an overview of experimental breakthroughs and areas of application
- Asymptotic role of entanglement in quantum metrology
- Multiple phase estimation for arbitrary pure states under white noise
- Coherent measurements in quantum metrology
- Optimal witnessing of the quantum Fisher information with few measurements
- Quantum key distribution with phase-encoded coherent states: Asymptotic security analysis in thermal-loss channels
- Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology
- Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
- Protecting quantum memories using coherent parity check codes
- Quantum Fisher information on two manifolds of two-mode Gaussian states
- Adaptive phase measurements for narrowband squeezed beams
- Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure
- Ancilla-Assisted Enhancement of Channel Estimation for Low-Noise Parameters
- Quantum metrology of spatial deformation using arrays of classical and quantum light emitters
- Linear optical quantum metrology with single photons --- Experimental errors, resource counting, and quantum Cramér-Rao bounds
- A tight Cramér-Rao bound for joint parameter estimation with a pure two-mode squeezed probe
- Reconstructing the Profile of Time-Varying Magnetic Fields With Quantum Sensors
- Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology
- Optimal Quantum Metrology of Distant Black Bodies
- Robustness of Quantum-Enhanced Adaptive Phase Estimation
- Finite-error metrological bounds on the multi-parameter Hamiltonian estimation
- The quantum Allan variance
- Quantum metrology including state preparation and readout times
- Optimal estimation of the optomechanical coupling strength
- Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems
- Noise-dependent optimal strategies for quantum metrology
- Enhancing sensitivity in quantum metrology by Hamiltonian extensions
- Experimental ancilla-assisted phase-estimation in a noisy channel
- Diamond Magnetometry of Meissner Currents in a Superconducting Film
- Thermal quantum metrology in memoryless and correlated environments
- Adaptive estimation and discrimination of Holevo-Werner channels
- Discrete-to-continuous transition in quantum phase estimation
- Optimal estimation of matter-field coupling strength in the dipole approximation
- Joint estimation of phase and phase diffusion for quantum metrology
Cited by in corpus (155)
- Advances in Space Quantum Communications
- Dynamical obstruction to localization in a disordered spin chain
- Quantum Plasmonic Sensors
- Fluctuations in extractable work bound the charging power of quantum batteries
- Fisher Information in Noisy Intermediate-Scale Quantum Applications
- Space-borne quantum memories for global quantum communication
- Tutorial: Optical quantum metrology
- Unifying Quantum and Classical Speed Limits on Observables
- Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
- Quantum Semiparametric Estimation
- Review: Quantum Metrology and Sensing with Many-Body Systems
- Optimal Scheme for Quantum Metrology
- The quantum limit to incoherent imaging is achieved by linear interferometry
- Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit
- Bayesian multi-parameter quantum metrology with limited data
- Tight bounds on the simultaneous estimation of incompatible parameters
- Quantum metrology for non-Markovian processes
- Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
- Quantum ranging with Gaussian entanglement
- QuanEstimation: An open-source toolkit for quantum parameter estimation
- Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
- Optimal Distributed quantum sensing using Gaussian states
- Quantum sensing networks for the estimation of linear functions
- Optimal and Variational Multi-Parameter Quantum Metrology and Vector Field Sensing
- Geometric distinguishability measures limit quantum channel estimation and discrimination
- Non-Markovian Sensing of a Quantum Reservoir
- Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology
- Extremal quantum states
- Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
- Fisher information universally identifies quantum resources
- Bayesian parameter estimation using Gaussian states and measurements
- Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
- Subwavelength quantum imaging with noisy detectors
- Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
- Optimal Generators for Quantum Sensing
- Multiphase estimation without a reference mode
- Single-photon sub-Rayleigh precision measurements of a pair of incoherent sources of unequal intensity
- Finite key performance of satellite quantum key distribution under practical constraints
- On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation
- Protocols for estimating multiple functions with quantum sensor networks: geometry and performance
- A quantitative comparison of amplitude versus intensity interferometry for astronomy
- Characterizing (non-)Markovianity through Fisher Information
- Information geometry under hierarchical quantum measurement
- Optimal Measurement of Field Properties with Quantum Sensor Networks
- Modular Many-Body Quantum Sensors
- Time-delayed single satellite quantum repeater node for global quantum communications
- Quantum theory of polarimetry: From quantum operations to Mueller matrices
- Experimental demonstration of topological bounds in quantum metrology
- Quantum scale estimation
- Approximate decoherence free subspaces for distributed sensing
- Inference-Based Quantum Sensing
- Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination
- Finite resource performance of small satellite-based quantum key distribution missions
- Taming singularities of the quantum Fisher information
- Current Trends in Global Quantum Metrology
- Quantum receiver for phase-shift keying at the single photon level
- Effects of coherence on temporal resolution
- Evading noise in multiparameter quantum metrology with indefinite causal order
- Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
- Thermodynamic principle for quantum metrology
- Activation of metrologically useful genuine multipartite entanglement
- Distributed quantum phase sensing for arbitrary positive and negative weights
- Sensing rotations with multiplane light conversion
- Optimizing illumination for precise multi-parameter estimations in coherent diffractive imaging
- Frequency estimation by frequency jumps
- Quantum metrology with a continuous-variable system
- Private and Robust States for Distributed Quantum Sensing
- Typicality of Heisenberg scaling precision in multi-mode quantum metrology
- Estimation of Hamiltonian parameters from thermal states
- Strict hierarchy of optimal strategies for global estimations: Linking global estimations with local ones
- Imaging arbitrary incoherent source distributions with near quantum-limited resolution
- Continuous-variable quantum sensing of a dissipative reservoir
- Quantum metrology in the finite-sample regime
- On the optimality of the radical-pair quantum compass
- Heisenberg scaling precision in multi-mode distributed quantum metrology
- Generating a 4-photon Tetrahedron State: Towards Simultaneous Super-sensitivity to Non-commuting Rotations
- Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
- Analysis of lower bounds for quantum control times and their relation to the quantum speed limit
- Unified entropies and quantum speed limits for nonunitary dynamics
- Nonlocality enhanced precision in quantum polarimetry via entangled photons
- Limited quantum advantage for stellar interferometry via continuous-variable teleportation
- Quantum Polarimetry
- First-principles construction of symmetry-informed quantum metrologies
- Resource-efficient simulation of noisy quantum circuits and application to network-enabled QRAM optimization
- Relative purity, speed of fluctuations, and bounds on equilibration times
- Super-Resolution Imaging with Multiparameter Quantum Metrology in Passive Remote Sensing
- Experimental investigation of Bayesian bounds in multiparameter estimation
- RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
- Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes
- Stochastic optimal control formalism for an open quantum system
- Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
- Performance-tradeoff relation for locating two incoherent optical point sources
- Optimal distributed multiparameter estimation in noisy environments
- Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
- Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
- Comparison of estimation limits for quantum two-parameter estimation
- Multiparameter transmission estimation at the quantum Cramér-Rao limit on a cloud quantum computer
- Quantum Estimation of the Stokes Vector Rotation for a General Polarimetric Transformation
- Simultaneous estimation of multiple phases in generalised Mach-Zehnder interferometer
- Multiparameter estimation with two qubit probes in noisy channels
- Non-equilibrium quantum probing through linear response
- Relative Phase Distribution and the Precision of Optical Phase Sensing in Quantum Metrology
- Heisenberg-Limited Spin-Mechanical Gravimetry
- Optimizing measurement tradeoffs in multiparameter spatial superresolution
- Bures geodesics and quantum metrology
- Quantum metrology of a structured reservoir
- Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
- Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
- Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space
- Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms
- Mixedness timescale in non-Hermitian quantum systems
- Optimal transmission estimation with dark counts
- Robust quantum metrology with random Majorana constellations
- Operation fidelity explored by numerical range of Kraus operators
- Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution
- Bayesian quantum phase estimation with fixed photon states
- Retrieving maximum information of symmetric states from their corrupted copies
- Randomized measurements for multi-parameter quantum metrology
- Quantum multiphase estimation
- Resource theory of dephasing estimation in multiqubit systems
- Quantum Measurement Encoding for Quantum Metrology
- Bayesian and frequentist estimators for the transition frequency of a driven two-level quantum system
- Selective and noise-resilient wave estimation with quantum sensor networks
- Evolved Quantum Boltzmann Machines
- Phase space contraction rate for classical mixed states
- Gaussian phase sensitivity of boson-sampling-inspired strategies
- Configuration-dependent precision in magnetometry and thermometry using multi-qubit quantum sensors
- Dynamics and multiqubit entanglement in distant resonators
- Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model
- Quantum metrology in a lossless Mach-Zehnder interferometer using entangled photon inputs
- Optimal and robust error filtration for quantum information processing
- Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
- Quantum Rabi interferometry of motion and radiation
- Describing quantum metrology with erasure errors using weight distributions of classical codes
- Ultimate Quantum Precision Limit at Colliders: Conditions and Case Studies
- Optimal quantum metrology under energy constraints
- Quantum natural gradient with thermal-state initialization
- Scaling Network Topologies for Multi-User Entanglement Distribution
- Natural gradient and parameter estimation for quantum Boltzmann machines
- Improved Quantum Sensing by Spectral Design
- Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
- Fluctuations in Extractable Work and Bounds on the Charging Power of Quantum Batteries
- Role of overparametrization in quantum approximate optimization
- Harnessing Floquet dynamics for selective metrology in few-qubit systems
- Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
- Direct temperature readout in nonequilibrium quantum thermometry
- Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
- Information geometry of bosonic Gaussian thermal states
- Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors
- Quantum illumination via frequency-mode-based correlation-to-displacement conversion
- Metrological Advantages in Seeded and Lossy Nonlinear Interferometers
- Quantum-enhanced passive remote sensing
- Bounding the benefit of adaptivity in quantum metrology using the relative fidelity
- Nonlocal Cancellation of Optical Rotations in Fructose Solutions
- Quantum Physics in Space