Optimal Quantum Phase Estimation

Abstract

By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

4 pages, 4 figures. Replaced with final version

References in corpus (11)

• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
• On the Improvement of Frequency Stardards with Quantum Entanglement
• Super-resolving phase measurements with a multi-photon entangled state
• Beating the Standard Quantum Limit with Four Entangled Photons
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Entanglement-free Heisenberg-limited phase estimation
• Time-reversal and super-resolving phase measurements
• Qubit metrology and decoherence
• Multiphoton path entanglement by non-local bunching
• Optimal estimation of one parameter quantum channels

Cited by in corpus (279)

• Advances in Quantum Metrology
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Advances in Photonic Quantum Sensing
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Quantum metrology with entangled coherent states
• Quantum limits in optical interferometry
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Squeezed states of light and their applications in laser interferometers
• Quantum enhanced measurements without entanglement
• Quantum Enhanced Multiple Phase Estimation
• Using entanglement against noise in quantum metrology
• Photonic polarization gears for ultra-sensitive angular measurements
• Quantum phase estimation with lossy interferometers
• Multi-parameter Quantum Metrology
• Experimental quantum-enhanced estimation of a lossy phase shift
• A Geometric Perspective on Quantum Parameter Estimation
• Optical phase estimation in the presence of phase-diffusion
• Quantum Coherence via Skew Information and Its Polygamy
• Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state
• Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
• Multi-parameter estimation beyond Quantum Fisher Information
• Quantum optical technologies for metrology, sensing and imaging
• Quantum interferometry with and without an external phase reference
• Optimal quantum-enhanced interferometry using a laser power source
• The ultimate precision limits for noisy frequency estimation
• Quantum metrology for a general Hamiltonian parameter
• Entanglement-enhanced probing of a delicate material system
• Efficient tools for quantum metrology with uncorrelated noise
• Ultimate precision bound of quantum and sub-wavelength imaging
• Phase sensing beyond the standard quantum limit with a truncated SU(1,1) interferometer
• Measuring protein concentration with entangled photons
• Phase matching condition for enhancement of phase sensitivity in quantum metrology
• Quantum Plasmonic Sensors
• Quantum metrology with imperfect states and detectors
• Phase-controlled integrated photonic quantum circuits
• A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
• Quantum Metrological Limits via a Variational Approach
• Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
• Not all pure entangled states are useful for sub shot-noise interferometry
• Qubit-excitation-based adaptive variational quantum eigensolver
• Real-world Quantum Sensors: Evaluating Resources for Precision Measurement
• Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles
• Phase estimation without a priori knowledge in the presence of loss
• Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
• The phase sensitivity of an SU(1,1) interferometer with homodyne detection
• Tutorial: Optical quantum metrology
• Efficient quantum circuits for quantum computational chemistry
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum
• Coherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit
• Bayesian quantum frequency estimation in presence of collective dephasing
• Quantum metrology for non-linear phase shifts with entangled coherent states
• Parity Measurement is Sufficient for Phase Estimation at the Quantum Cramer-Rao Bound for Path-Symmetric States
• Optimization of quantum interferometric metrological sensors in the presence of photon loss
• Experimental Phase Estimation Enhanced By Machine Learning
• Phase estimation for thermal Gaussian states
• Quantum-enhanced metrology for multiple phase estimation with noise
• Robust quantum metrological schemes based on protection of quantum Fisher information
• Optical interferometry in the presence of large phase diffusion
• Optimal Scheme for Quantum Metrology
• Tuneable quantum interference in a 3D integrated circuit
• Optimal Measurement on Noisy Quantum Systems
• Parity Detection in Quantum Optical Metrology Without Number Resolving Detectors
• Entanglement in fermion systems and quantum metrology
• Entanglement-enhanced optical gyroscope
• Practical route to entanglement-assisted communication over noisy bosonic channels
• Approaching optimal entangling collective measurements on quantum computing platforms
• Retrieving ideal precision in noisy quantum optical metrology
• Quantum metrology in the presence of limited data
• Sub-shot-noise quantum metrology with entangled identical particles
• Super-Resolution at the Shot-Noise Limit with Coherent States and Photon-Number-Resolving Detectors
• Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
• Quantum states made to measure
• Efficient optical quantum state engineering
• Quantum-enhanced interferometry with large heralded photon-number states
• Quantum plasmonic sensing: beyond the shot-noise and diffraction limit
• Nearly Optimal Measurement Scheme in a Noisy Mach-Zehnder Interferometer with Coherent and Squeezed Vacuum
• Dissipative Quantum Metrology with Spin Cat States
• Phase sensitivity of a Mach-Zehnder interferometer with single-intensity and difference-intensity detection
• Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge
• Multiparameter quantum estimation of noisy phase shifts
• Enhanced interferometry using squeezed thermal states and even or odd states
• Phase sensitivity bounds for two-mode interferometers
• QuanEstimation: An open-source toolkit for quantum parameter estimation
• Super-Resolving Quantum Radar: Coherent-State Sources with Homodyne Detection Suffice to Beat the Diffraction Limit
• Entangling measurements for multiparameter estimation with two qubits
• Quantum metrology for the Ising Hamiltonian with transverse magnetic field
• Quantum multi-parameter estimation with generalized balanced multi-mode NOON-like states
• Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
• Relativistic Quantum Metrology in Open System Dynamics
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Entanglement enhanced atomic gyroscope
• Gaussian interferometric power
• Thresholded Quantum LIDAR -- Exploiting Photon-Number-Resolving Detection
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
• Optimized phase sensing in a truncated SU(1,1) interferometer
• Phase estimation via quantum interferometry for noisy detectors
• Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer
• Matrix product states for quantum metrology
• Quantum interferometry with binary-outcome measurements in the presence of phase diffusion
• Deterministic Super Resolution with Coherent States at the Shot Noise Limit
• Quantum noise reduction in intensity-sensitive surface plasmon resonance sensors
• Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology
• Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations
• Single- versus two-parameter Fisher information in quantum interferometry
• Quantum metrology: why entanglement?
• Investigating macroscopic quantum superpositions and the quantum-to-classical transition by optical parametric amplification
• Optimal experiment design revisited: fair, precise and minimal tomography
• Quantum metrology beyond Heisenberg limit with entangled matter wave solitons
• Optimal Mach-Zehnder phase sensitivity with Gaussian states
• Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
• Strategies for choosing path-entangled number states for optimal robust quantum optical metrology in the presence of loss
• Multi-mode Entanglement is Detrimental to Lossy Optical Quantum Metrology
• Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
• Maximal quantum Fisher information for general su(2) parametrization processes
• Mode engineering for realistic quantum-enhanced interferometry
• Weak measurements and the joint estimation of phase and phase diffusion
• Quantum metrology in a non-Markovian quantum evolution
• Lossy Quantum Optical Metrology with Squeezed States
• Practical resources and measurements for lossy optical quantum metrology
• Parameter estimation with cluster states
• Quantum limit for measurement of a weak classical force coupled to a noisy quantum-mechanical oscillator
• Unbounded quantum Fisher information in two-path interferometry with finite photon number
• Fisher information of a squeezed-state interferometer with a finite photon-number resolution
• Integrated Photonic Sensing
• Spontaneous parametric downconversion in waveguides: What's loss got to do with it?
• Electromagnetic shielding in quantum metrology
• Effects of loss on the phase sensitivity with parity detection in an SU(1,1) interferometer
• Robust quantum enhanced phase estimation in a multimode interferometer
• Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit
• Quantum Optical Metrology of Correlated Phase and Loss
• Enhanced Resolution of Lossy Interferometry by Coherent Amplification of Single Photons
• Zeno dynamics in quantum open systems
• Sub-Heisenberg-limited nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound
• Attaining sub-classical metrology in lossy systems with entangled coherent states
• Entangled and sequential quantum protocols with dephasing
• Quantum limit for laser interferometric gravitational wave detectors from optical dissipation
• Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology
• Experimental quantum polarimetry using heralded single photons
• Quantum metrology in the noisy intermediate-scale quantum era
• Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment
• Optical phase estimation via coherent state and displaced photon counting
• Quantum enhanced spectroscopy with entangled multi-photon states
• Optimal entangled coherent states in lossy quantum-enhanced metrology
• Quantum correlation measure in arbitrary bipartite systems
• Metrology with Unknown Detectors
• Phase estimation by photon counting measurements in the output of a linear Mach Zehnder (MZI) interferometer
• Quantum computation speedup limits from quantum metrological precision bounds
• Non-asymptotic Heisenberg scaling: experimental metrology for a wide resources range
• Latency considerations for stochastic optimizers in variational quantum algorithms
• Supersensitivity of Kerr phase estimation with two-mode squeezed vacuum states
• Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment
• Phase sensitivity for an unbalanced interferometer without input phase-matching restrictions
• Near-Heisenberg-limited parameter estimation precision by a dipolar-Bose-gas reservoir engineering
• Noise-dependent optimal strategies for quantum metrology
• The Quantum-Classical Boundary for Precision Interferometric Measurements
• Mitigating quantum decoherence in force sensors by internal squeezing
• Transmission Estimation at the Cramér-Rao Bound for Squeezed States of Light in the Presence of Loss and Imperfect Detection
• Quantum-enhanced Phase Estimation with an Amplified Bell State
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses
• Quantum Enhanced Phase Retrieval
• Noise limits on two-photon interferometric sensing
• SU(1,1)-type light-atom correlated interferometer
• Robustness of Heisenberg-limited interferometry with balanced Fock states
• Thermodynamic work cost of quantum estimation protocols
• Quantum Gaussian filter for exploring ground-state properties
• Multiparameter estimation via an ensemble of spinor atoms
• Experimental ancilla-assisted phase-estimation in a noisy channel
• Double-port measurements for robust quantum optical metrology
• Amplification of polarization NOON states
• Noisy quantum gyroscope
• Multi-pass classical vs. quantum strategies in lossy phase estimation
• Precision bounds for noisy nonlinear quantum metrology
• Generation of phase-squeezed optical pulses with large coherent amplitudes by post-selection of single photon and weak cross-Kerr non-linearity
• Loss-resistant unambiguous phase measurement
• Entanglement in Algebraic Quantum Mechanics: Majorana fermion systems
• Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons
• Data processing over single-port homodyne detection to realize super-resolution and super-sensitivity
• Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation
• Optimal multiple-phase estimation with multi-mode NOON states against photon loss
• The best Fisher is upstream: data processing inequalities for quantum metrology
• High-dimensional cryptographic quantum parameter estimation
• Optimizing Passive Quantum Clocks
• Engineering mesoscopic superpositions of superfluid flow
• Estimation of general Hamiltonian parameters via controlled energy measurements
• Bell inequality for pairs of particle-number-superselection-rule restricted states
• Distributed quantum sensing with multi-mode $N00N$ states
• Discrete-to-continuous transition in quantum phase estimation
• Photonic quantum metrology with variational quantum optical non-linearities
• Ordered Measurements of Permutationally-Symmetric Qubit Strings
• Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms
• Non-Markovian effect on quantum optical metrology under dissipative environment
• Enhancing test precision for local Lorentz symmetry violation with entanglement
• Phase Estimation with Non-Unitary Interferometers: Information as a Metric
• Phase Estimation from Atom Position Measurements
• Preservation of quantum Fisher information and geometric phase of a single qubit system in a dissipative reservoir through the addition of qubits
• Effects of local decoherence on quantum critical metrology
• Super-Sensitive Ancilla-Based Adaptive Quantum Phase Estimation
• The probe readout and quantum limited measurements
• Multi-outcome homodyne detection in a coherent-state light interferometer
• Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution
• Fundamental sensitivity limit of lossy cavity-enhanced interferometers with external and internal squeezing
• Enhancing the precision limits of interferometric satellite geodesy missions
• Weakly invasive metrology: quantum advantage and physical implementations
• Dissipative quantum light field engineering
• Optical interferometer using two-mode squeezed light for enhanced chip-integrated quantum metrology
• Probing Bayesian credible regions intrinsically: a feasible error certification for physical systems
• Quantum superreplication of states and gates
• Optimal lossy quantum interferometry in phase space
• Diagnosing Imperfections in Quantum Sensors via Generalized Cramér-Rao Bounds
• Bayesian error regions in quantum estimation II: region accuracy and adaptive methods
• Noise assisted Ramsey interferometry
• Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing
• Optimal quantum phase estimation in an atomic gyroscope based on Bose-Hubbard model
• Noisy Metrology: A saturable lower bound on quantum Fisher information
• Enhancing precision of atomic clocks by tuning disorder in accessories
• Variational Limits for Phase Precision in Linear Quantum Optical Metrology
• Quantum techniques for eigenvalue problems
• Quantum-enhanced joint estimation of phase and phase diffusion
• Multiparameter estimation with two qubit probes in noisy channels
• Theoretical studies on quantum imaging with time-integrated single-photon detection under realistic experimental conditions
• Implementation of traveling odd Schr$\ddot{o}$dinger cat states in circuit-QED
• Goldilocks Probes for Noisy Interferometry via Quantum Annealing to Criticality
• Quantum-Limited Estimation of Phase Gradient
• Enhancing precision of damping rate by PT symmetric Hamiltonian
• Enhancing parameter estimation precision in dissipative environment with two-photon driving
• On the role of symmetry and geometry in global quantum sensing
• Sensing performance enhancement via asymmetric gain optimization in the atom-light hybrid interferometer
• Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
• Bayesian minimum mean square error for transmissivity sensing
• Bayesian quantum phase estimation with fixed photon states
• Persistent quantum advantage with definite photon-number states in lossy multiple-phase estimation
• Entanglement of condensed magnons via momentum-space fragmentation
• Generalized phase estimation in noisy quantum gates
• Quantum metrology in a lossless Mach-Zehnder interferometer using entangled photon inputs
• Time-adaptive phase estimation
• Non-asymptotic quantum metrology
• Globally optimal interferometry with lossy twin Fock probes
• Quantum metrology and its application in biology
• Simultaneous optical phase and loss estimation revisited: measurement and probe incompatibility
• Unified strategy for non-invertible Fisher information matrix in quantum metrology
• Enhanced frequency estimation by non-Gaussianity of Fock states
• Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
• Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Phase-retrieval from Bohm's equations
• Sub-shot-noise interferometry with two-mode quantum states
• Quantum enhanced estimation of optical detector efficiencies
• Optimal circular dichroism sensing with quantum light: Multi-parameter estimation approach
• Bosonic Entanglement and Quantum Sensing from Energy Transfer in two-tone Floquet Systems
• Recovering optimal precision in quantum sensing with time domain imperfections
• Adaptive random compiler for Hamiltonian simulation
• Multi-ion Mach-Zehnder interferometer with artificial nonlinear interactions
• Holevo Cramér-Rao bound: How close can we get without entangling measurements?
• Joint estimation of phase and phase diffusion for quantum metrology
• Quantum-like nonlinear interferometry with frequency-engineered classical light
• Precise Phase Measurements using an Entangled Coherent State
• Numerical investigation of the quantum inverse algorithm on small molecules
• Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry
• Optimal noisy quantum phase estimation with finite-dimensional states
• Rigorous no-go theorems for heralded linear-optical state generation tasks
• Dissipative Quantum Metrology
• Quantum Sensors: Improved Optical Measurement via Specialized Quantum States
• Universal Operational Privacy in Distributed Quantum Sensing
• Non-Markovianity-based ultrasensitive parameter estimation
• Power of photonic states: from quantum computation to cosmology
• Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements
• Fluctuation-guided adaptive random compiler for Hamiltonian simulation
• Phase Diffusion of Light Immersed In Quantum Tides: Open Quantum System Approach
• Measurement compatibility in multiparameter quantum interferometry
• Kramers-Kronig relations and precision limits in quantum phase estimation
• Protecting spin squeezing from decoherence
• Optimal Hamiltonian recognition of unknown quantum dynamics
• Quantum interferometry at zero and finite temperature with two-mode bosonic Josephson junctions
• Quantum Parameter Estimation for Detectors in Constantly Accelerated Motion
• Optimal finite-dimensional probe states for quantum phase estimation
• Quantum Speedups for Multiproposal MCMC