Simultaneous multiple angular displacement estimation precision enhanced by the intramode correlation

TL;DR

This paper explores how intramode correlation in probe states enhances the precision of simultaneous multiple angular displacement estimation using quantum optical methods, especially under noisy conditions.

Contribution

It introduces a framework utilizing (d + 1)-mode NOON-like states and reveals the positive impact of intramode correlation on estimation precision, including robustness improvements.

Findings

Intramode correlation improves quantum Cramer-Rao bound (QCRB) performance.

Multimode entangled squeezed vacuum states outperform other probe states.

Increasing OAM quantum number enhances robustness against photon losses.

Abstract

The angular displacement estimation is one of significant branches of quantum parameter estimation. However, most of the studies have focused on the single-angular displacement estimation, while the multiple angular displacement estimation in ideal and noisy scenarios is still elusive. In this paper, we investigate the simultaneous multiple angular displacement estimation based on an orbital angular momentum (OAM), together with inputting (d + 1)-mode NOON-like states as the probe state. By revealing the role of the intramode correlation of the probe state, this allows us to give a reasonable explanation for the corresponding quantum Cramer-Rao bound (QCRB) behaviors with and without photon losses. Our analyses suggest that the QCRB for the multiple angular displacement estimation is always positively related to the intramode correlation, especially for the multimode entangled squeezed vacuum state showing the best performance compared to another probe state. More importantly, strengthening the robustness of multiple angular-displacement estimation systems can be achieved by increasing the OAM quantum number.