Using the world’s largest data samples of 10 billion $\jpsi$ and 2.7 billion $\psi(3686)$ data samples collected at the BESIII experiment, large entangled hyperon-antihyperon pairs are produced.The transverse polarization of hyperons is observed in the $\jpsi$ and $\psi(3686)$ decays, which provides an excellent opportunity to search for $CP$ violation in hyperon decays.Meanwhile, the large hyperon samples provide a promising avenue for measurements of rare hyperon decays, such as hyperon weak radiative decays.