  We study the transport properties of a quantum dot-Majorana hybrid system, in
which each of paired Majorana bound states is connected to one quantum dot.
With the help of non-equilibrium Green's function method, we obtain an exact
solution of the Green's functions and calculate the currents through the
quantum dots and nonlocal noise cross correlation between the currents. As a
function of dot energy levels $\epsilon_{1}$ and $\epsilon_{2}$, we find that
for the symmetric level configuration $\epsilon_{1}=\epsilon_{2}$, the noise
cross correlation is negative in the low lead voltage regime, while it becomes
positive with the increase of the lead voltages. Due to the particle-hole
symmetry, the cross correlation is always positive in the anti-symmetric case
$\epsilon_{1}=-\epsilon_{2}$. In contrast, the cross correlation of
non-Majorana setups is always positive. For comparison, we also perform the
diagonalized master equation calculation to check its applicability. It is
found that the diagonalized master equations work well in most regimes of
system parameters. Nevertheless, it shows an obvious deviation from the exact
solution by the non-equilibrium Green's function method when all eigenenergies
of the dot-Majorana hybrid system and simultaneously the energy intervals are
comparable to the dot-lead coupling strength.
