  We investigate the spin density matrix of $\Omega^-$ in the Cartesian
coordinate system of baryon-antibaryon pairs produced in $e^{+}e^{-}$
annihilation. Using the helicity formalism of Jacob and Wick, we derive the
expression for the spin-3/2 density matrices. Our analysis is based on the
angular distribution of the process
$e^+e^-\rightarrow\psi(3686)\rightarrow\Omega^-\bar{\Omega}^+$ in the BESIII
experiment. By decomposing the polarization state of $\Omega^-$ particles along
different coordinate axes, we examine the polarization dependence of the
cross-section. Our results demonstrate that $\Omega^-$ particles exhibit
varying degrees of tensor polarization along the x-, y-, and z-axes, as well as
weak vector polarization and rank-3 tensor polarization along the y-axis. To
our knowledge, this is the first study to calculate the polarization dependence
of the cross-section distributions for the annihilation process
$e^+e^-\rightarrow\Omega^-\bar{\Omega}^+$. Our theoretical predictions are in
good agreement with the experimental measurements.
