The internal nonlocality in general dilated Hermiticity

$\cal PT$-symmetric systems can be viewed as effective models in the sense of open systems. This allows people to simulate a $\cal PT$-symmetric system by dilating it to a global Hermitian one. Recently, the internal nonlocality in such dilated Hermitian systems was discussed for a special case with some two fold structure. In this paper, we extend such a discussion to the general case, by utilizing a general property of Hermitian dilation Hamiltonians. Different correlation pictures are proposed and the corresponding correlation bounds are obtained.