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The angular displacement estimation is one of significant branches of quantumparameter estimation. However, most of the studies have focused on thesingle-angular displacement estimation, while the multiple angular displacementestimation in ideal and noisy scenarios is still elusive. In this paper, weinvestigate the simultaneous multiple angular displacement estimation based onan orbital angular momentum (OAM), together with inputting (d + 1)-modeNOON-like states as the probe state. By revealing the role of the intramodecorrelation of the probe state, this allows us to give a reasonable explanationfor the corresponding quantum Cramer-Rao bound (QCRB) behaviors with andwithout photon losses. Our analyses suggest that the QCRB for the multipleangular displacement estimation is always positively related to the intramodecorrelation, especially for the multimode entangled squeezed vacuum stateshowing the best performance compared to another probe state. More importantly,strengthening the robustness of multiple angular-displacement estimationsystems can be achieved by increasing the OAM quantum number.

Simultaneous multiple angular displacement estimation precision enhanced by the intramode correlation