The spin observables of a polarized reaction obey spin inequalities translating the positivity of the cross section matrix, which is the density matrix of a state gathering all the polarized particles (initial and final ones).
This « quantum positivity » is more severe than the mere « classical positivity » of the cross section. We give their physical meaning in terms of separable or entangled states and compare their respective domains in the space of observables.
In a second part, we recall the Knowless-Collins rules for Monte-Carlo generation of polarized and entangled cascades and tell how to apply them in the recursive jet model and in e+e- annihilation into hadrons.