Simultaneous multiple angular displacement estimation precision enhanced by the intramode correlation

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 Cramér-Rao bound (QCRB) behaviors. Our analyses suggest that the QCRB for 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.