Parity Measurement is Sufficient for Phase Estimation at the Quantum Cramer-Rao Bound for Path-Symmetric States

TL;DR

This paper demonstrates that measuring photon number parity in path-symmetric states achieves optimal phase estimation at the quantum Cramer-Rao bound, enabling precise local phase measurements in optical interferometry.

Contribution

It proves that parity measurement is sufficient for optimal phase estimation at the quantum Cramer-Rao bound for all path-symmetric states.

Findings

Parity measurement achieves maximal phase sensitivity at the quantum Cramer-Rao bound.

Optimal phase sensitivity occurs at a known bias phase.

The scheme is applicable for local phase estimation.

Abstract

In this letter, we show that for all the so-called path-symmetric states, the measurement of parity of photon number at the output of an optical interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao bound. Such optimal phase sensitivity with parity is attained at a suitable bias phase, which can be determined a priori. Our scheme is applicable for local phase estimation.