Optimal estimation of multiple phases

Abstract

We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular, we discuss the explicit case of the optimal detection of double phase for a system of identical qutrits and generalise these results to optimal multiple phase detection for d-dimensional quantum states.

6 pages

References in corpus (4)

• Security of quantum key distribution using d-level systems
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Optimal phase covariant cloning for qubits and qutrits
• Cloning a Qutrit

Cited by in corpus (31)

• Quantum Enhanced Multiple Phase Estimation
• Multi-parameter Quantum Metrology
• A Geometric Perspective on Quantum Parameter Estimation
• Optimal measurements for simultaneous quantum estimation of multiple phases
• Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
• Quantum Cloning Machines and the Applications
• Economical Phase-Covariant Cloning of Qudits
• Experimental multiphase estimation on a chip
• Bayesian multi-parameter quantum metrology with limited data
• Multiparameter quantum estimation of noisy phase shifts
• Probe incompatibility in multiparameter noisy quantum metrology
• Quantum sensing networks for the estimation of linear functions
• Entanglement is not very useful for estimating multiple phases
• The role of entanglement in calibrating optical quantum gyroscopes
• Multiple phase estimation for arbitrary pure states under white noise
• Quantum phases of a qutrit
• Multiple phase estimation in quantum cloning machines
• Standard Quantum Limit and Heisenberg Limit in Function Estimation
• Experimental multiparameter quantum metrology in adaptive regime
• Finite-error metrological bounds on the multi-parameter Hamiltonian estimation
• Optimal probabilistic estimation of quantum states
• Quantum scale estimation
• Taming singularities of the quantum Fisher information
• A complementarity-based approach to phase in finite-dimensional quantum systems
• A protocol for global multiphase estimation
• Experimental investigation of Bayesian bounds in multiparameter estimation
• Optimal Time-Reversal of Multi-phase Equatorial States
• Economical realization of phase covariant devices in arbitrary dimensions
• Non-asymptotic quantum metrology
• Quantum multiphase estimation
• The Cramér-Rao approach and global quantum estimation of bosonic states