  The difference in the properties of the spin correlation tensor for
factorizable and nonfactorizable two-particle states is analyzed. The
inequalities for linear combinations of the components of this tensor are
obtained for the case of incoherent mixtures of factorizable two-particle spin
states. They include the well known Bell inequalities and can be violated for
coherent superpositions of two-particle spin states. The possibility to verify
the consequences of the quantum-mechanical coherence is discussed using the
angular correlations in the asymmetric (parity violating) decays of the pairs
of spin-1/2 particles (muons, top-quarks or lambda-hyperons), the coherence
arising either from the production dynamics or due to the effect of quantum
statistics.
