  It is a common problem in lattice QCD calculation of the mass of the hadron
with an annihilation channel that the signal falls off in time while the noise
remains constant. In addition, the disconnected insertion calculation of the
three-point function and the calculation of the neutron electric dipole moment
with the $\theta$ term suffer from a noise problem due to the $\sqrt{V}$
fluctuation. We identify these problems to have the same origin and the
$\sqrt{V}$ problem can be overcome by utilizing the cluster decomposition
principle. We demonstrate this by considering the calculations of the glueball
mass, the strangeness content in the nucleon, and the CP violation angle in the
nucleon due to the $\theta$ term. It is found that for lattices with physical
sizes of 4.5 - 5.5 fm, the statistical errors of these quantities can be
reduced by a factor of 3 to 4. The systematic errors can be estimated from the
Akaike information criterion. For the strangeness content, we find that the
systematic error is of the same size as that of the statistical one when the
cluster decomposition principle is utilized. This results in a 2 to 3 times
reduction in the overall error.
