  A general and in principle exact approach for the continuous variable
entanglement in a system of coupled harmonic oscillators in contact with a
thermal bath is formulated. This allows a generalization to describe
entanglement's existence between two sites in any system of this kind. It is
employed a method of simultaneous diagonalization of two quadratic forms to
obtain the uncoupled quantum Hamiltonian. Making use of the transformations
that uncouple the system, the covariance matrix for two positions is
constructed, and through the positive partial transpose criterion
(PPT-criterion), the condition that determines the existence or not of quantum
correlation between the sites is obtained.
