  The Bell nonlocality and entanglement are two kinds of quantum correlations
in quantum systems. Due to the recent upgrade in Beijing Spectrometer III
(BESIII) experiment, it is possible to explore the nonlocality and entanglement
in hyperon-antihyperon systems produced in electron-positron annihilation with
high precision data. We provide a systematic method for studying quantum
correlations in spin-1/2 hyperon-antihyperon systems through the measures for
the nonlocality and entanglement. We find that with nonvanishing polarizations
of the hyperon and its antihyperon, the kinematic region of nonlocality in the
hyperon-antihyperon system is more restricted than the $\tau^{+}\tau^{-}$
system in which polarizations of $\tau$ leptons are vanishing. We also present
an experimental proposal to probe the nonlocality and entanglement in
hyperon-antihyperon systems at BSEIII.
