Optimal phase measurements with pure Gaussian states

Abstract

We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive local measurement schemes that attain the Heisenberg limit asymptotically. One of them is described by a positive operator-valued measure and its efficiency is exhaustively explored. We also study Gaussian measurement schemes based on phase quadrature measurements. We show that homodyne tomography of the appropriate quadrature attains the Heisenberg limit for large samples. This proves that this limit can be attained with local projective Von Neuman measurements.

9 pages. Revised version: two new sections added, revised conclusions. Corrected prose. Corrected references

References in corpus (7)

• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• State estimation for large ensembles
• A new approach to the Cramer-Rao type bound of the pure state model
• Fisher information in quantum statistics
• Adaptive single-shot phase measurements: The full quantum theory
• Parameters estimation in quantum optics
• Estimation of pure qubit states with collective and individual measurements

Cited by in corpus (96)

• Advances in Quantum Metrology
• Quantum criticality as a resource for quantum estimation
• Quantum parameter estimation using general single-mode Gaussian states
• Quantum parameter estimation using general single-mode Gaussian states
• Optical phase estimation in the presence of phase-diffusion
• Optimal quantum estimation of loss in bosonic channels
• Optimal estimation of joint parameters in phase space
• Quantum Plasmonic Sensors
• Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control
• Multiparameter Gaussian Quantum Metrology
• Qubit thermometry for micromechanical resonators
• Simple expression for the quantum Fisher information matrix
• Estimation of Gaussian quantum states
• Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
• Optimal probe states for the estimation of Gaussian unitary channels
• Phase estimation for thermal Gaussian states
• Quantum thermometry by single-qubit dephasing
• Optical interferometry in the presence of large phase diffusion
• Optimal Scheme for Quantum Metrology
• Quantum probes for the spectral properties of a classical environment
• Quantum probes for the cutoff frequency of Ohmic environments
• Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology
• Characterization of classical Gaussian processes using quantum probes
• Squeezed vacuum as a universal quantum probe
• Bayesian estimation in homodyne interferometry
• Continuous-variable quantum probes for structured environments
• Optimal estimation of entanglement
• QuanEstimation: An open-source toolkit for quantum parameter estimation
• Phase sensitivity bounds for two-mode interferometers
• Relativistic Quantum Metrology in Open System Dynamics
• Sub-Heisenberg estimation of non-random phase-shifts
• Information geometry of Gaussian channels
• Learning feedback control strategies for quantum metrology
• Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point
• Deterministic quantum phase estimation beyond the ideal NOON state limit
• Characterization of qubit chains by Feynman probes
• Quantum Phase Estimation with Entangled Photons produced by Parametric Down Conversion
• Coherent measurements in quantum metrology
• Designing quantum experiments with a genetic algorithm
• Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied
• On the optimal feedback control of linear quantum systems in the presence of thermal noise
• Deterministic phase measurements exhibiting super-sensitivity and super-resolution
• Characterization of quantum angular-momentum fluctuations via principal components
• Squeezing by Critical Speeding-up: Applications in Quantum Metrology
• The power of one qumode for quantum computation
• Quantum Probes for Ohmic Environments at Thermal Equilibrium
• Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit
• Enhancement of parameter estimation by Kerr interaction
• Beyond coincidence: using all the data in Hong-Ou-Mandel interferometry
• Quantum Fisher information matrix in Heisenberg XY model
• Entangled and sequential quantum protocols with dephasing
• Thermometry of Gaussian quantum systems using Gaussian measurements
• Universal quantum magnetometry with spin states at equilibrium
• Improving the estimation of environment parameters via initial probe-environment correlations
• Protection of noise squeezing in a quantum interferometer with optimal resource allocation
• Optical phase estimation via coherent state and displaced photon counting
• Non-Orthogonal Bases for Quantum Metrology
• Squeezing-enhanced communication without a phase reference
• Unconditional mechanical squeezing via back-action evading measurements and non-optimal feedback control
• Heisenberg scaling precision in the estimation of functions of parameters
• Optimal Conventional Measurements for Quantum-Enhanced Interferometry
• Quantum metrology at level anti-crossing
• Quantum metrology with a continuous-variable system
• Quantum-enhanced screened dark energy detection
• Precision bounds for noisy nonlinear quantum metrology
• Typicality of Heisenberg scaling precision in multi-mode quantum metrology
• Estimating space-time parameters with a quantum probe in a lossy environment
• Squeezing as a resource to counteract phase diffusion in optical phase estimation
• Quantum detection of wormholes
• Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation
• Heisenberg scaling precision in multi-mode distributed quantum metrology
• Generating nonlinearities from conditional linear operations, squeezing and measurement for quantum computation and super-Heisenberg sensing
• Relativistic quantum clocks
• Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
• Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction
• Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation
• Efficient qubit phase estimation using adaptive measurements
• Phase variance of squeezed vacuum states
• Phase Estimation with Non-Unitary Interferometers: Information as a Metric
• Nonlinear fiber gyroscope for quantum metrology
• Phononic gravity gradiometry with Bose-Einstein condensates
• Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements
• Continuous-variable phase-estimation with unitary and random linear disturbance
• Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit
• Average number is an insufficient metric for interferometry
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• General quantum phase estimation and calibration of a timepiece in a quantum dot system
• Quantum phase estimation using squeezed quasi-Bell states
• Gaussian phase sensitivity of boson-sampling-inspired strategies
• Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
• Phase-sensitive nonclassical properties in quantum metrology with a displaced squeezed vacuum state
• Optimality of Gaussian receivers for practical Gaussian distributed sensing
• Power of photonic states: from quantum computation to cosmology
• Quantum enhanced optical phase estimation with a squeezed thermal state
• Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
• Knowledge-dependent optimal Gaussian strategies for phase estimation