  Spin polarization and entanglement are utilized by the BESIII experiment to
learn more about the production and decay properties of hyperon-antihyperon
pairs in a series of recent analyses of its unprecedented datasets at the
$J/\psi$ and $\psi'$ resonances. This has lead to the observation of
significant transverse polarisation in decays of $J/\psi$ or $\psi'$ into
$\Lambda \bar{\Lambda}$, $\Sigma \bar{\Sigma}$, $\Xi \bar{\Xi}$, and $\Omega
\bar{\Omega}$. Because of the non-zero polarization, the decay parameters for
the most common hadronic weak decays of both hyperons and antihyperons could be
determined independently for the first time. Comparing these to each other
yields precise tests of direct, $\Delta S = 1$ CP-violation that complement
measurements of kaon decays.
