Bell inequality is violated in $B^0\to J/\psi \, K^{\star}(892)^0$ decays

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 Bell inequality that it entails. We find that the violation has a significance of 36$\sigma$-- thereby firmly establishing this distinguishing feature of quantum mechanics at high energies in a collider setting and in the presence of strong and weak interactions. The Bell inequality is also violated in other decays of the $B$ mesons into vector mesons, but with lesser significance.