Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases

TLDR

Quantum multiphase estimation theory is essential for quantum‑enhanced sensing and imaging and may connect quantum metrology to advanced quantum computation and communication protocols. The study addresses the challenge of finding measurements that achieve the fundamental sensitivity limits in multiphase estimation. The authors derive necessary and sufficient conditions for projective measurements on pure states to saturate the quantum Fisher information matrix bound and demonstrate the theory with photon‑number measurements in interferometric phase estimation. These results provide new concepts and methods that will guide future theoretical and experimental work in multiparameter estimation.

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 ultimate 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.