The measurement of quantum entanglement can provide a new and most sensitive probe to physics beyond the Standard Model. We use the concurrence of the top-quark pair spin states produced at colliders to constrain the magnetic dipole term in the coupling between top quark and gluons, that of $\tau$-lepton pairs spin states to bound contact interactions and that of $\tau$-lepton pairs or two-photons spin states from the decay of the Higgs boson in trying to distinguish between CP-even and odd couplings. These four examples show the power of the new approach as well as its limitations. We show that differences in the entanglement in the top-quark and $\tau$-lepton pair production cross sections can provide constraints better than those previously estimated from total cross sections or classical correlations. Instead, the final states in the decays of the Higgs boson remain maximally entangled even in the presence of CP odd couplings and cannot be used to set bounds on new physics. We discuss the violation of Bell inequalities featured in all four processes.