  The observation of the vector meson's global spin alignment by the STAR
Collaboration reveals that strong spin correlations may exist for quarks and
antiquarks in relativistic heavy-ion collisions in the normal direction of the
reaction plane. We propose a systematic method to describe such correlations in
the quark matter. The correlations can be classified as local and long range
types. We show in particular that the effective quark spin correlations contain
the genuine spin correlations originated directly from the dynamical process as
well as those induced by averaging over other degrees of freedom. We also show
that such correlations can be studied by measuring the vector meson's spin
density matrix and hyperon-hyperon and hyperon-anti-hyperon spin correlations.
We present the relationships between these measurable quantities and spin
correlations of quarks and antiquarks.
