Spin correlation of hyperon-antihyperon systems in $e^+e^-$ annihilation

Quantum correlations in high-energy collisions provide a novel perspective on both fundamental physics and hadron structure. We calculate the quantum information observable in spin-1/2 particle-antiparticle systems produced in $e^+e^-$ annihilation. Starting from the two-qubit density operator, we calculate the Bell variable, concurrence and negativity as functions of the scattering angle and collision energy for the $\Lambda\bar{\Lambda}$, $\Sigma^+\bar{\Sigma}^-$, and $\Lambda^+_c\bar{\Lambda}^-_c$ systems in the process $e^+e^-\rightarrow B\bar{B}$ at BESIII experiments. Unlike elementary particle-antiparticle systems, the hyperon-antihyperon system exhibits non-vanishing transverse polarization for $B$ and $\bar{B}$ with respect to the production plane, which significantly restrict the kinematic region where the CHSH inequality is violated while leaving the entanglement largely unaffected. We also extend our analysis to the general case of spin-1/2 particle-antiparticle production, and explore the potential of using quantum correlations as probes to hadron structure, particularly to the parton-level entanglement inside heavy-flavored mesons.