The Quantum-Classical Boundary for Precision Interferometric Measurements

TL;DR

This paper investigates the fundamental quantum limits of optical phase measurement precision, comparing classical and non-classical strategies, and finds that non-classical methods offer limited improvements in realistic multi-pass optical setups with losses.

Contribution

The study quantifies the maximum achievable precision enhancement of non-classical states over classical states in optical phase estimation, especially considering realistic multi-pass and lossy conditions.

Findings

Non-classical techniques provide less than 20% RMSE reduction in ideal multi-pass setups.

In a new classical setup with additional interference stages, non-classical benefits drop to about 4%.

Photon losses significantly diminish the advantage of non-classical states in practical scenarios.

Abstract

Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase shift due to a sample which has an associated optical loss, and compare phase estimation strategies using classical and non-classical probe states. These comparisons are based on the attainable (quantum) Fisher information calculated per number of photons absorbed or scattered by the sample throughout the sensing process. We find that, for a given number of incident photons upon the unknown phase, non-classical techniques in principle provide less than a 20% reduction in root-mean-square-error (RMSE) in comparison with ideal classical techniques in multi-pass optical setups. Using classical techniques in a new optical setup we analyze, which incorporates additional stages of interference during the sensing process, the achievable reduction in RMSE afforded by non-classical techniques falls to only ~4%. We explain how these conclusions change when non-classical techniques are compared to classical probe states in non-ideal multi-pass optical setups, with additional photon losses due to the measurement apparatus.