Quantum metrology from a quantum information science perspective

Abstract

We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.

43 pages, 9 figures; v4: typos corrected, published version; special issue "50 years of Bell's theorem"

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• Collectively enhanced quantum measurements at the Heisenberg limit
• Matrix product states for quantum metrology
• Quantum Phase Estimation with Entangled Photons produced by Parametric Down Conversion
• Feedback-cooling of an atomic spin ensemble
• Local temperature in quantum thermal states
• Quantum Metrology with Cold Atoms
• Quantum-circuit guide to optical and atomic interferometry
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• Fundamental limits to frequency estimation: A comprehensive microscopic perspective
• Nonclassical Light and Metrological Power: An Introductory Review
• Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
• Massive quantum systems as interfaces of quantum mechanics and gravity
• Multipartite Entanglement at Finite Temperature
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• Improving cold-atom sensors with quantum entanglement: Prospects and challenges
• Quantum repeaters in space
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• Correlation-based entanglement criterion in bipartite multiboson systems
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Characterizing the width of entanglement
• Simultaneous estimation of multiple phases in generalised Mach-Zehnder interferometer
• Maximally entangled Rydberg-atom pairs via Landau-Zener sweeps
• A survey of universal quantum von Neumann architecture
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Role of indistinguishability in interferometric phase estimation
• Mutual Information Bounded by Fisher Information
• Qubit-assisted quantum metrology under a time-reversal strategy
• Bipartite Bound Entanglement
• Detecting Macroscopic Indefiniteness of Cat States in Bosonic Interferometers
• Experimental demonstration of optimal probabilistic enhancement of quantum coherence
• Erasure conversion for singlet-triplet spin qubits enables high-performance shuttling-based quantum error correction
• Quantum metrology of a structured reservoir
• Goldilocks Probes for Noisy Interferometry via Quantum Annealing to Criticality
• Backpropagation scaling in parameterised quantum circuits
• Entanglement of Local Hidden States
• Complementarity between decoherence and information retrieval from the environment
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics
• Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation
• Indefinite Time Directed Quantum Metrology
• Detecting coherence with respect to general quantum measurements
• Experimental single-copy distillation of quantumness from higher-dimensional entanglement
• Simultaneous quantum estimation of phase and indistinguishability in a two photon interferometer
• Bayesian Quantum Amplitude Estimation
• Entanglement detection in quantum materials with competing orders
• Multipartite entanglement structure of monitored quantum circuits
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Homodyne detection is optimal for quantum interferometry with path-entangled coherent states
• Two dimensional arrays of Bose-Einstein condensates: interference and stochastic collapse dynamics
• Distributed multi-parameter quantum metrology with a superconducting quantum network
• Optimizing quantum sensing networks via genetic algorithms and deep learning
• Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of $s$-spin coherent states
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Sub-Poissonian atom-number distributions by means of Rydberg dressing and electromagnetically induced transparency
• Average number is an insufficient metric for interferometry
• Two-colour spectrally multimode integrated SU(1,1) interferometer
• Robust quantum metrology with random Majorana constellations
• Quantum thermometry in diffraction-limited systems
• Quantum-enhanced mean value estimation via adaptive measurement
• Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk
• Multipartite States under Elementary Local Operations
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Spin-bounded correlations: rotation boxes within and beyond quantum theory
• Thermometry with a Dissipative Heavy Impurity
• Existence of unbiased resilient estimators in discrete quantum systems
• Many-body quantum metrology with scalar bosons in a single potential well
• Optimal quantum sensing of the nonlinear bosonic interactions using Fock states
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Autonomous Stabilization of Floquet States Using Static Dissipation
• Entangled states from sparsely coupled spins for metrology with neutral atoms
• From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
• Control of open quantum systems: Manipulation of a qubit coupled to a thermal bath by an external driving field
• Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits
• Asymmetry-induced nonclassical correlation
• Measurement-Based Entanglement Distillation and Constant-Rate Quantum Repeaters over Arbitrary Distances
• Gaussian phase sensitivity of boson-sampling-inspired strategies
• Quantum resources of the steady-state of three coupled qubits: Microscopic versus Phenomenological model
• Non-Gaussian Dissipative Quantum Thermometry Beyond Gaussian Bounds
• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• Resource theory of dephasing estimation in multiqubit systems
• Machine-learning-inspired quantum control in many-body dynamics
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
• Better Heisenberg limits, coherence bounds, and energy-time tradeoffs via quantum Rényi information
• Achieving the Heisenberg limit of metrology via measurement on an ancillary qubit
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures
• Configuration-dependent precision in magnetometry and thermometry using multi-qubit quantum sensors
• Dynamics of quantum resources in regular and Majorana fermion systems
• Quantum Advantage in Distributed Sensing with Noisy Quantum Networks
• Nonclassical states of light in a nonlinear Michelson interferometer
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Anonymous and private parameter estimation in networks of quantum sensors
• Quantum Information Measures in Quartic and Symmetric Potentials using perturbative approach
• Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model
• Current-based metrology with two-terminal mesoscopic conductors
• Dephasing effects on quantum correlations and teleportation in presence of state dependent bath
• Uncertainty relations between quantum Fisher information and entanglement monotones
• Single-shot Adaptive Measurement for Quantum-enhanced Metrology
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• Determination of spatial quantum states by using Point Diffraction Interferometry
• Unraveling quantum phase estimation: exploring the impact of multi-photon interference on the quantum Fisher information
• Robustness of the projected squeezed state protocol
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Bosonic Entanglement and Quantum Sensing from Energy Transfer in two-tone Floquet Systems
• Quantum metrology through spectral measurements in quantum optics
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Many-spin entanglement in multiple quantum NMR with a dipolar ordered initial state
• Holevo Cramér-Rao bound: How close can we get without entangling measurements?
• Improving quantum walk metrology with split-step quantum walk
• An atomic Fabry-Perot interferometer-based acceleration sensor for microgravity environments
• Explicit noise and dissipation operators for quantum stochastic thermodynamics
• Ultimate Quantum Precision Limit at Colliders: Conditions and Case Studies
• Coherence-Mediated Quantum Thermometry in a Hybrid Circuit-QED Architecture
• Unlocking Heisenberg Sensitivity with Sequential Weak Measurement Preparation
• Enhancement of the metrological sensitivity limit through knowledge of the average energy
• Quantum Limits of Position and Polarizability Estimation in the Optical Near Field
• A protocol to create a multi-particle entangled state for quantum-enhanced sensing
• Error estimation of different schemes to measure spin-squeezing inequalities
• Opportunities and Limitations in Broadband Sensing
• Towards scalable active steering protocols for genuinely entangled state manifolds
• The genuinely multipartite nonlocality of graph states is model-dependent
• Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth
• Quantum Fisher information from tensor network integration of Lyapunov equation
• Golden states in resource theory of superposition
• Detecting high-dimensional entanglement by randomized product projections
• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Trade-off relation between integrated metrological gain and local dissipation in magnetic-field sensing by quantum spin ensemble
• Knowledge-dependent optimal Gaussian strategies for phase estimation
• Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution
• Chaos-Mediated Quantum State Discrimination Near Unit Fidelity
• Scaling laws for the sensitivity enhancement of non-Gaussian spin states
• Quantum illumination via frequency-mode-based correlation-to-displacement conversion
• Optimal finite-dimensional probe states for quantum phase estimation
• Complete $k$-partite entanglement measure
• Discrete time crystal for periodic-field sensing with quantum-enhanced precision
• Coherence and Entanglement in a Non-commutative Spacetime
• QMetro++ -- Python optimization package for large scale quantum metrology with customized strategy structures
• Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Modified Quantum Wheatstone Bridge based on current circulation
• Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
• Probing parameters estimation with Gaussian non-commutative measurements
• Sub-Bath Cooling in Bosonic Systems: Gaussian Constraints and Non-Gaussian Enhancements
• Witnessing Spin-Orbital Entanglement using Resonant Inelastic X-Ray Scattering
• Characterization and generation of a SQL-beating catlike state through repetitive measurements
• Dynamical Maps for Accelerating Detectors
• Graphene Josephson Junctions for Engineering Motional Quanta
• Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry
• State-independent uncertainty relations on multipartite spin $1/2$-systems
• From Independent to Joint: Enhancing Quantum Phase and Correlation Factor Estimation by Squeezed Reservoir Engineering
• Informationally Complete Distributed Metrology Without a Shared Reference Frame
• Multipartite entangled states in dipolar quantum simulators
• Bending the rules of low-temperature thermometry with periodic driving
• Decoherence and objectivity in higher spin environments
• Toward Witnessing Molecular Exciton Entanglement from Spectroscopy
• Optimal spin- and planar-quantum squeezing in superpositions of spin coherent states
• Measuring entanglement along collective operators
• Reference-frame-independent quantum metrology