  We have shown the covariant relativistic spin operator is equivalent to the
spin operator commuting with the free Dirac Hamiltonian. This implies that the
covariant relativistic spin operator is a good quantum observable. The
covariant relativistic spin operator has the pure quantum contribution which
does not exist in the classical covariant spin operator. Based on this
equivalence reduced spin states can be claerly defined. We have shown the
change in the entropy of a reduced spin density matrix sweeps through the whole
range according to the relative motion of an observer.
