Tests of CP symmetry in entangled hyperon anti-hyperon pairs at BESIII

Decays of charmonium into hyperon and antihyperon pairs provide a pristine laboratory for exploring hyperon properties, such as their polarization and decay parameters, and for conducting tests of fundamental symmetries. This brief review highlights the significant progress made in precise tests of CP symmetry at BESIII using entangled hyperon-antihyperon pairs, including $\Lambda\bar{\Lambda}$, $\Sigma\bar{\Sigma}$, $\Xi\bar{\Xi}$ and $\Lambda\bar{\Sigma}$, selected from the high statistics of $J/\psi$ and $\psi(3686)$ events produced in $e^+e^-$ annihilations. These recent findings have sparked renewed interest in both theoretical and experimental aspects of hyperon physics, but there is still much room for improvement to reach the Standard Model expectations. To address this challenge, the prospects for future investigations on CP asymmetry at next-generation experiments are discussed.