Canonical Phase Measurements in the Presence of Photon Loss

TL;DR

This paper investigates the impact of photon loss on canonical phase measurements, providing exact density matrix calculations to determine the maximum photon number for sub-shot noise precision.

Contribution

It offers a direct, approximation-free analysis of the optimal quantum state under photon loss in phase measurements, extending previous theoretical work.

Findings

Derived the upper bound for input photon number with photon loss

Provided exact density matrix calculations for the model

Identified conditions for sub-shot noise estimation

Abstract

We analyze the optimal state, as given by Berry and Wiseman [Phys. Rev. Lett {\bf 85}, 5098, (2000)], under the canonical phase measurement in the presence of photon loss. The model of photon loss is a generic fictitious beam splitter, and we present the full density matrix calculations, which are more direct and do not involve any approximations. We find for a given amount of loss the upper bound for the input photon number that yields a sub-shot noise estimate.