  We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin
I=0 system from Lattice QCD. In order to solve this system, we prepare three
types of baryon-baryon operators ($\Lambda-\Lambda$, $N-\Xi$ and
$\Sigma-\Sigma$) for the sink and construct three source operators
diagonalizing the $3\times3$ correlation matrix. Combining of the prepared sink
operators with the diagonalized source operators, we obtain nine effective
Nambu-Bethe-Salpeter (NBS) wave functions. The $3\times3$ potential matrix is
calculated by solving the coupled-channel Schr\"odinger equation. The flavor
SU(3) breaking effects of the potential matrix are also discussed by comparing
with the results of the SU(3) limit calculation. Our numerical results are
obtained from three sets of 2+1 flavor QCD gauge configurations provided by the
CP-PACS/JLQCD Collaborations.
