All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry

TL;DR

This paper demonstrates that all path-symmetric pure states in two-path interferometers can reach their maximum phase sensitivity, achieving the quantum Cramer-Rao bound regardless of the phase bias, due to their symmetry properties.

Contribution

It establishes that path symmetry in pure states guarantees maximal phase sensitivity in conventional two-path interferometry, extending understanding of quantum phase estimation.

Findings

Path-symmetric pure states achieve the quantum Cramer-Rao bound.

Maximal phase sensitivity is attainable at any phase bias.

Path symmetry is conserved under phase shifts.

Abstract

It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path symmetry is conserved under phase shifts, the maximal phase sensitivity can be achieved at arbitrary bias phases, indicating that path symmetric states can achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely unknown phase.