  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.
