  The experimental data on the helicity amplitudes of charmonium decays allow
us to measure entanglement in final state spin correlations and test possible
violations of the Bell inequality. We find that the Bell inequality is violated
with a significance of 5$\sigma$ or more in the decays
  $\eta_{c}, \, \chi_{c}^{0}, \, J/\psi \to \Lambda +\bar \Lambda$
  $J/\psi \to \Xi^- +\bar \Xi^+,\; \Xi^0 +\bar \Xi^0, \;\Sigma^{-} +\bar
\Sigma^{+},\; \Sigma^{0} +\bar \Sigma^{0}$,
  $\psi(3686) \to \Xi^- +\bar \Xi^+,\; \Sigma^- +\bar \Sigma^+,\; \Sigma^{0}
+\bar \Sigma^{0}$,
  $\chi^{0}_{c}, \, \chi_{c}^{1} \to \phi+ \phi$ .
  The decays $\psi(3686) \to \Lambda +\bar \Lambda$ and $\Xi^0 +\bar \Xi^0$
show the same violation but with less significance. The decay $\psi(3686) \to
\Omega^- + \bar \Omega^+$ displays entanglement. These results firmly establish
the presence of entanglement and quantum non-separability at high energies, in
a setting with particles of different spins and interacting through electroweak
and strong interactions. In addition, the relatively long lifetime of some of
the strange baryons produced in the decays provides a natural probe to test
whether quantum spin correlations remain after the particles have interacted
with the beam pipe and the first few layers of the detector.
