Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge

Abstract

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap in the literature on the subject which until now dealt almost exclusively with two extreme cases: almost perfect knowledge (local approach based on Fisher information) and no a priori knowledge (global approach based on covariant measurements). Special attention is paid to a natural a priori probability distribution arising from a diffusion process.

4 pages, 2 figures (final version)

References in corpus (7)

• Reference frames, superselection rules, and quantum information
• Optimal Quantum Phase Estimation
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
• Phase estimation without a priori knowledge in the presence of loss
• Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
• Local and Global Distinguishability in Quantum Interferometry

Cited by in corpus (41)

• A Geometric Perspective on Quantum Parameter Estimation
• Quantum interferometry with and without an external phase reference
• Efficient tools for quantum metrology with uncorrelated noise
• True precision limits in quantum metrology
• Bayesian quantum frequency estimation in presence of collective dephasing
• Flexible resources for quantum metrology
• Global Quantum Thermometry
• Bayesian multi-parameter quantum metrology with limited data
• Quantum metrology in the presence of limited data
• QuanEstimation: An open-source toolkit for quantum parameter estimation
• Quantum sensing networks for the estimation of linear functions
• Tensor-Network Approach for Quantum Metrology in Many-Body Quantum Systems
• Optimal Quantum States for Image Sensing in Loss
• Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
• Symmetric M-ary phase discrimination using quantum-optical probe states
• Precision bounds in noisy quantum metrology
• Quantum scale estimation
• Optimal quantum-state tomography with known parameters
• Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
• Improved sensing with a single qubit
• Quantum metrology in the finite-sample regime
• Optimizing Passive Quantum Clocks
• Noisy distributed sensing in the Bayesian regime
• First-principles construction of symmetry-informed quantum metrologies
• Discrete-to-continuous transition in quantum phase estimation
• No-signaling bounds for quantum cloning and metrology
• Average number is an insufficient metric for interferometry
• Bayesian quantum phase estimation with fixed photon states
• Numerical test of few-qubit clock protocols
• Perfect quantum protractors
• Time-adaptive phase estimation
• Non-asymptotic quantum metrology
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Adaptive tomography of qubits: Purity versus statistical fluctuations
• Adaptive, symmetry-informed Bayesian metrology for precise quantum technology measurements
• Optimality of Gaussian receivers for practical Gaussian distributed sensing
• Quantum Fisher Information: Variational principle and simple iterative algorithm for its efficient computation
• QMetro++ -- Python optimization package for large scale quantum metrology with customized strategy structures
• Improved Quantum Sensing by Spectral Design
• Optimal noisy quantum phase estimation with finite-dimensional states
• High-precision estimation of the parameters in the reservoir via the two-level system