With the large datasets from $e^+e^-$ annihilation at the $J/\psi$ and $\psi(3686)$ resonances collected at the BESIII experiment, multi-dimensional analyses leveraging polarization and entanglement can provide new insights into the production and decay properties of hyperon-antihyperon pairs. Recent studies at BESIII have revealed significant transverse polarization of the (anti)hyperons in the decays $J/\psi$ or $\psi(3686)\to\Lambda\bar{\Lambda}$, $\Sigma\bar{\Sigma}$, and $\Xi\bar{\Xi}$.

The decay parameters for the most common hadronic weak decay modes have been measured. Thanks to the non-zero polarization, the decay parameters for hyperons and antihyperons could be determined independently for the first time. Comparing these decay parameters allows for precise tests of direct $\Delta S=1$ CP violation, complementing studies conducted in the kaon sector.