Optimal probabilistic measurement of phase

TL;DR

This paper investigates the limits of probabilistic quantum measurements for phase estimation, aiming to maximize precision at a given success rate through optimal measurement strategies and noiseless amplification.

Contribution

It introduces a framework for determining the optimal probabilistic measurement that enhances phase measurement precision under success probability constraints.

Findings

Optimal probabilistic measurement strategies identified

Maximum phase precision achieved for given success rates

Limits of noiseless amplification in phase measurement analyzed

Abstract

When measuring phase of quantum states of light, the optimal single-shot measurement implements projection on the un-physical phase states. If we want to improve the precision further we need to accept a reduced probability of success, either by implementing a probabilistic measurement or by probabilistically manipulating the measured quantum state by means of noiseless amplification. We analyze the limits of this approach by finding the optimal probabilistic measurement which, for a given rate of success, maximizes the precision with which the phase can be measured.