  With the aim of clarification of color correlations among quarks, we
investigate the color correlation between a static quark and an antiquark
(static $q\bar q$) below and above the phase transition temperature $T_c$
through the entanglement entropy(EE). By a quenched lattice QCD calculation on
an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb
gauge, we compute a reduced density matrix $\rho$ defined in the color space,
and the entanglement entropy $S_{\rm EE}$ constructed from $\rho$. The spatial
volume is $L^3 = 24^3$ and the temporal extents are $N_T =
12,13,14,15,16,18,20$ and $24$, with a gauge coupling $\beta = 5.75$ and a
renormalized anisotropy $\xi = 4.0$, which corresponds to temperatures between
180 and 370 MeV. From an analysis of $\rho$ and $S_{\rm EE}$, the color
correlation between $q\bar q$ pairs is obtained as a function of the interquark
distance $R$ and the temperature $T$. Below $T_c$, the $R$-dependence of the
color correlation resembles that at $T=0$: the quark's color correlation
gradually decreases as $R$ increases due to the color screening by in-between
gluons. Above $T_c$, due to the deconfinement phase transition, the color
correlation among quarks is found to quickly dissappear. Further, we
investigate the color screening effect via the screening mass defined by
$\rho$, and discuss the differences in the screening properties between the
small and large R regions.
