  The violation of the Bell inequality is one of the hallmarks of quantum
mechanics and can be used to rule out local deterministic alternative
descriptions. We utilize the data analysis published by the LHCb collaboration
on the helicity amplitudes for the decay $B^0\to J/\psi \,K^*(892)^0$ to
compute the entanglement among the polarizations of the final vector mesons and
the violation of the Bell inequality that it entails. We find that quantum
entanglement can be detected with a significance well above 5$\sigma$
(nominally 84$\sigma$) and Bell inequality is violated with a significance well
above 5$\sigma$ (nominally 36$\sigma$) -- thereby firmly establishing these
distinguishing feature of quantum mechanics at high energies in a collider
setting and in the presence of strong and weak interactions. Entanglement is
also present and the Bell inequality is violated in other decays of the $B$
mesons into vector mesons, but with lesser significance.
