  The BESIII detector on the BEPCII collider collected the world's largest
dataset at the peaks of $J/\psi$, $\psi(3686)$ and $\psi(3770)$. The use of
polarization and entanglement states in multidimensional angular distribution
analysis can provide new probes to the production and decay characteristics of
hyperon anti hyperon pairs. In a recent series of studies, significant
transverse polarization in hyperon decay has been observed in $J/\psi$,
$\psi(3686)$ decaying into the $\Lambda\bar\Lambda$, $\Sigma^+\bar\Sigma^{-}$,
$\Xi^0\bar\Xi^0$ and $\Xi^-\bar\Xi^{+}$ final states. The weak decay parameters
of hyperons and antihyperons are also independently determined for the first
time. The most accurate testing for direct $CP$ violation has been achieved
based on the measured weak decay parameters.
