Quantum-correlation of neutral charmed mesons at BESIII

BESIII has recently collected a large data sample at the $\psi$(3770) energy point, with an integrated luminosity of 20 $\textrm{fb}^{-1}$. The neutral $D^{0}\bar{D}^{0}$ pairs produced at $\psi$(3770) are in a C-odd correlated state, offering a unique laboratory for measuring the strong-phase differences between $D^{0}$ and $\bar{D}^{0}$ decays. These parameters are crucial inputs for $C\!P$-violation studies in heavy-flavor physics, such as determining the CKM angle $\gamma$ and charm-mixing parameters, searching for indirect $C\!P$ violtion in the charm sector. In this presentation, we report recent progresses on new or improved measurements of the strong-phase differences in various neutral $D$ decays at BESIII. We also present results on the $C\!P$-even fractions for multi-body decays. Finally, we discuss measurements of strong phase difference from additional $D^{0}\bar{D}^{0}$ pairs produced at 4180 MeV.