Optimal measurements for simultaneous quantum estimation of multiple phases

Abstract

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this letter we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the maximal theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

4 pages + appendix, 2 figures

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• Fisher Information and entanglement of non-Gaussian spin states
• Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
• Robust Online Hamiltonian Learning
• Optimal estimation of joint parameters in phase space
• Quantum interferometry with three-dimensional geometry
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Cited by in corpus (5)

• Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
• Control-enhanced multiparameter quantum estimation
• Experimental multiphase estimation on a chip
• Optimal joint estimation of multiple Rabi frequencies
• Time Evolution and Thermodynamics for the Nonequilibrium System in Phase-Space