Generalized Limits for Single-Parameter Quantum Estimation

Abstract

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.

4 pages, 1 figure. v2 typos corrected

References in corpus (8)

• Quantum metrology
• Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Quantum Superposition States of Bose-Einstein Condensates
• Exponentially Enhanced Quantum Metrology
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Efficient one-step generation of large cluster states with solid-state circuits
• Phase Sensitivity of a Mach-Zehnder Interferometer

Cited by in corpus (256)

• Advances in Quantum Metrology
• Quantum metrology with nonclassical states of atomic ensembles
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Quantum metrology from a quantum information science perspective
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum Fisher information matrix and multiparameter estimation
• Enhancing the charging power of quantum batteries
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Quantum speed limit for physical processes
• Quantum enhanced measurements without entanglement
• Improved quantum metrology using quantum error-correction
• Prospective applications of optical quantum memories
• Achieving the Heisenberg limit in quantum metrology using quantum error correction
• Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
• A Geometric Perspective on Quantum Parameter Estimation
• Quantum Metrology: Dynamics vs. Entanglement
• General optimality of the Heisenberg limit for quantum metrology
• Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
• Fundamental Quantum Limit to Waveform Estimation
• Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
• Thermometry in the quantum regime: Recent theoretical progress
• Exponentially Enhanced Quantum Metrology
• Quantum metrology for a general Hamiltonian parameter
• Arbitrarily Accurate Dynamical Control in Open Quantum Systems
• Optimal and Secure Measurement Protocols for Quantum Sensor Networks
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• Quantum Fisher information for states in exponential form
• Digital Quantum Simulation of Minimal AdS/CFT
• Quantum Plasmonic Sensors
• Adaptive quantum metrology under general Markovian noise
• Not all pure entangled states are useful for sub shot-noise interferometry
• Single-Mode Displacement Sensor
• Ziv-Zakai Error Bounds for Quantum Parameter Estimation
• Qubit metrology and decoherence
• At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
• Time-information uncertainty relations in thermodynamics
• Parameter estimation of quantum channels
• Tutorial: Optical quantum metrology
• Quantum-limited metrology with product states
• Generation of Large Number-Path Entanglement Using Linear Optics and Feed-Forward
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Entanglement-assisted weak value amplification
• Nonlinear quantum metrology of many-body open systems
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Quantum limits on post-selected, probabilistic quantum metrology
• A nonlinear Ramsey interferometer operating beyond the Heisenberg limit
• Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit
• Entanglement-Enhanced Quantum Metrology in Colored Noise by Quantum Zeno Effect
• Flexible resources for quantum metrology
• Quantum metrology with unitary parametrization processes
• Sub-Heisenberg estimation strategies are ineffective
• Nonlinear quantum metrology using coupled nanomechanical resonators
• Quantum-enhanced metrology for multiple phase estimation with noise
• Global sensing and its impact for quantum many-body probes with criticality
• Random bosonic states for robust quantum metrology
• Quantum frequency estimation with trapped ions and atoms
• An operational interpretation for multipartite entanglement
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Ultimate limits to quantum metrology and the meaning of the Heisenberg limit
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Entanglement in fermion systems and quantum metrology
• Universality of the Heisenberg limit for estimates of random phase shifts
• Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
• Quantum-limited metrology and Bose-Einstein condensates
• Bayesian estimation of one-parameter qubit gates
• Phase transitions in an Ising chain interacting with a single mode cavity field
• Heisenberg scaling in Gaussian quantum metrology
• Precision Limits in Quantum Metrology with Open Quantum Systems
• Fundamental Sensitivity Limits for non-Hermitian Quantum Sensors
• Quantum Speed Limit for States with a Bounded Energy Spectrum
• Maximal Quantum Fisher Information for Mixed States
• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
• Quantum limited measurements of atomic scattering properties
• Quantum Metrology: Extended Convexity of Quantum Fisher Information
• Variational principle for optimal quantum controls in quantum metrology
• Single shot parameter estimation via continuous quantum measurement
• Nonlinear metrology with a quantum interface
• Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
• Entanglement is not a critical resource for quantum metrology
• Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point
• Free-Fermionic Topological Quantum Sensors
• Strong quantum metrological limit from many-body physics
• Distributed Quantum Metrology with a Single Squeezed-Vacuum Source
• Asymptotic role of entanglement in quantum metrology
• Quantum metrology with non-equilibrium steady states of quantum spin chains
• Quantum Phase Estimation with Entangled Photons produced by Parametric Down Conversion
• Parameter Estimation with Mixed-State Quantum Computation
• Quantum metrology of two-photon absorption
• Optimal witnessing of the quantum Fisher information with few measurements
• Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied
• How difficult is it to prepare a quantum state?
• Optimal estimation with quantum optomechanical systems in the nonlinear regime
• Experimental demonstration of cheap and accurate phase estimation
• Squeezing by Critical Speeding-up: Applications in Quantum Metrology
• Quantum metrology beyond Heisenberg limit with entangled matter wave solitons
• Sequential measurements for quantum-enhanced magnetometry in spin chain probes
• Control of inhomogeneous atomic ensembles of hyperfine qudits
• Criticality-enhanced quantum sensing in ferromagnetic Bose-Einstein condensates: role of readout measurement and detection noise
• Locally Optimal Control of Quantum Systems with Strong Feedback
• Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
• Parameter estimation with cluster states
• Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits
• Exponential precision by reaching a quantum critical point
• One from many: Estimating a function of many parameters
• Magnetometry via a double-pass continuous quantum measurement of atomic spin
• Improved thermometry of low-temperature quantum systems by a ring-structure probe
• Electromagnetic shielding in quantum metrology
• Stark localization as a resource for weak-field sensing with super-Heisenberg precision
• Mach Zehnder Interferometry with NOON Quantum States
• Nonlinear interferometry with Bose-Einstein condensates
• Discrete Time Crystal Phase as a Resource for Quantum Enhanced Sensing
• Dissipative quantum metrology in manybody systems of identical particles
• Achieving sub-shot-noise sensing at finite temperatures
• An eternal discrete time crystal beating the Heisenberg limit
• Sub Shot-Noise interferometric phase sensitivity with Beryllium ions Schroedinger Cat States
• Zeno dynamics in quantum open systems
• Sub-Heisenberg-limited nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound
• Protocols for estimating multiple functions with quantum sensor networks: geometry and performance
• Magnetic Sensitivity and Entanglement Dynamics of the Chemical Compass
• Localization Driven Quantum Sensing
• Continuity of the quantum Fisher information
• Entangled and sequential quantum protocols with dephasing
• Hybrid quantum-classical approach to enhanced quantum metrology
• Self-consistent many-body metrology
• Quantum metrology in the noisy intermediate-scale quantum era
• Optimal Measurement of Field Properties with Quantum Sensor Networks
• Fundamental limits of metrology at thermal equilibrium
• Quantum Model Averaging
• Experimental demonstration of topological bounds in quantum metrology
• Heisenberg-limited estimation robust to detector inefficiency in a multi-parameter Mach-Zehnder network with squeezed light
• Many-body effects in quantum metrology
• Quantum-circuit guide to optical and atomic interferometry
• Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes
• Supersensitivity of Kerr phase estimation with two-mode squeezed vacuum states
• Experimental Quantum Enhanced Optical Interferometry
• Intrinsic metrological resolution as a distance measure and nonclassical light
• Error-transparent evolution: the ability of multi-body interactions to bypass decoherence
• Quantum metrology using time-frequency as quantum continuous variables: Resources, sub shot-noise precision and phase space representation
• Completely positive classical structures and sequentializable quantum protocols
• Bounding Quantum Advantages in Postselected Metrology
• Distributed quantum phase sensing for arbitrary positive and negative weights
• Enhanced Quantum Metrology with Non-Phase-Covariant Noise
• Thermodynamic principle for quantum metrology
• Enhancing sensitivity in quantum metrology by Hamiltonian extensions
• Quantum parameter-estimation of frequency and damping of a harmonic-oscillator
• Long-range interacting Stark many-body probes with Super-Heisenberg precision
• Geometric aspects of analog quantum search evolutions
• Quantum limited measurement of space-time curvature with scaling beyond the conventional Heisenberg limit
• Energy-efficient quantum frequency estimation
• Frequency estimation by frequency jumps
• Quantum metrology with a continuous-variable system
• Multiqubit matter-wave interferometry under decoherence and the Heisenberg scaling recovery
• Exponentially-enhanced quantum sensing with many-body phase transitions
• Progress and Perspectives on Weak-value Amplification
• Precision bounds for noisy nonlinear quantum metrology
• Universal shot-noise limit for quantum metrology with local Hamiltonians
• Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation
• Entanglement in Algebraic Quantum Mechanics: Majorana fermion systems
• Quantifying the difference between many-body quantum states
• Number-unconstrained quantum sensing
• Generating nonlinearities from conditional linear operations, squeezing and measurement for quantum computation and super-Heisenberg sensing
• The best Fisher is upstream: data processing inequalities for quantum metrology
• Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology
• Nonlinear Michelson interferometer for improved quantum metrology
• Nonlinearity-enhanced quantum sensing in Stark probes
• Beating the classical phase precision limit using a quantum neuromorphic platform
• Scale-invariant spin dynamics and the quantum limits of field sensing
• Heisenberg scaling with classical long-range correlations
• Remote Tomography Via von Neumann-Arthurs-Kelly Interaction
• Stochastic waveform estimation at the fundamental quantum limit
• Quantum Metrology in the Kerr Metric
• Intrinsic measurement errors for the speed of light in vacuum
• Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation
• Phase variance of squeezed vacuum states
• Classical and quantum metrology of the Lieb-Liniger model
• Quantum metrology with precision reaching beyond-$1/N$ scaling through $N$-probe entanglement generating interactions
• Limited-control metrology approaching the Heisenberg limit without entanglement preparation
• Approaching maximal precision of Hong-Ou-Mandel interferometry with non-perfect visibility
• Enhancing precision thermometry with nonlinear qubits
• Nonlinear fiber gyroscope for quantum metrology
• Fundamental noisy multiparameter quantum bounds
• The probe readout and quantum limited measurements
• Minimum Entanglement Protocols for Function Estimation
• Optimal measurement precision of a nonlinear interferometer
• Probabilistic metrology or how some measurement outcomes render ultra-precise estimates
• Restoring metrological quantum advantage of measurement precision in noisy scenario
• How to find optimal quantum states for optical micromanipulation and metrology in complex scattering problems: tutorial
• Lower Bounds for Quantum Parameter Estimation
• Heisenberg-limited metrology with perturbing interactions
• Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices
• Noise assisted Ramsey interferometry
• Parameter estimation of wormholes beyond the Heisenberg limit
• Information Geometric Aspects of Probability Paths with Minimum Entropy Production for Quantum State Evolution
• A single atom noise probe operating beyond the Heisenberg limit
• Probabilistic metrology defeats ultimate deterministic bound
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Enhancing Quantum Metrology by Quantum Resonance Dynamics
• Quantum-enhanced atomic gyroscope with tunable precision
• Relations between quantum metrology and criticality in general su(1, 1) systems
• Quantum-enhanced sensing with variable-range interactions
• Achieving Heisenberg scaling by probe-ancilla interaction in quantum metrology
• Parametrized protocol achieving the Heisenberg limit in the optical domain via dispersive atom-light interactions
• Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
• Quantum Critical Environment Assisted Quantum Magnetometer
• Dynamic quantum-enhanced sensing without entanglement in central spin systems
• Quantum U-statistics
• Conditioned spin and charge dynamics of a single electron quantum dot
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Michelson interferometer for measuring temperature
• Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of $s$-spin coherent states
• Optimal function estimation with photonic quantum sensor networks
• Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
• Many-body quantum metrology with scalar bosons in a single potential well
• Maximal Entanglement and Teleportation using an Arthurs-Kelly type Interaction for Qubits
• Wasserstein Complexity of Quantum Circuits
• Quantum sensing of even- versus odd-body interactions
• Optimal quantum sensing of the nonlinear bosonic interactions using Fock states
• Cooperation between coherent control and noises in quantum metrology
• The Quantum Frontier
• From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
• Parameter Estimation, Model Reduction and Quantum Filtering
• Achieving the Heisenberg limit of metrology via measurement on an ancillary qubit
• Gaussian phase sensitivity of boson-sampling-inspired strategies
• Better Heisenberg limits, coherence bounds, and energy-time tradeoffs via quantum Rényi information
• Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology
• Quantum Measurement Encoding for Quantum Metrology
• Multiparameter quantum metrology using strongly interacting spin systems
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Affinity-based geometric discord and quantum speed limits of its creation and decay
• Quantum Metrology via Repeated Quantum Nondemolition Measurements in "Photon Box"
• An upper bound on the number of compatible parameters in simultaneous quantum estimation
• Atom-Molecule Superradiance and Entanglement with Cavity-Mediated Three-Body Interactions
• Nonclassical states of light in a nonlinear Michelson interferometer
• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Noisy Stark probes as quantum-enhanced sensors
• Quantum Fisher information matrix for unitary processes: closed relation for $SU(2)$
• Normal state quantum geometry, non-locality and superconductivity
• Nonlinear-enhanced wideband sensing via subharmonic excitation of a quantum harmonic oscillator
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• Phase Transitions in Light-Matter Systems for Quantum Sensing
• Thresholded Quantum Sensing with a Frustrated Kitaev Trimer
• Super-Heisenberg-limited Sensing via Collective Subradiance in Waveguide Quantum Electrodynamics
• Corrections to the expected signal in quantum metrology using highly anisotropic Bose-Einstein Condensates
• Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
• Quantum enhanced precision in a collective measurement
• Discrete time crystal for periodic-field sensing with quantum-enhanced precision
• Precision limit under weak coupling with an ancillary qubit
• Amplified Quantum Dynamics and Enhanced Parameter Sensitivity via Coherent Feedback in Collective Atomic Spin Systems
• Floquet quantum multiparameter estimation with periodic-driving-induced topological phase transition
• Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors
• Quantum Transition Rates in Arbitrary Physical Processes
• Quantum information with conserved quantities
• Reference-frame-independent quantum metrology
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation
• Quantum Information Processing with Continuous Variables and Atomic Ensembles