  We address the problem of removing correlation from sets of states while
preserving as much local quantum information as possible. We prove that states
obtained from universal cloning can only be decorrelated at the expense of
complete erasure of local information (i.e. information about the copied
state). We solve analytically the problem of decorrelation for two qubits and
two qumodes (harmonic oscillators in Gaussian states), and provide sets of
decorrelable states and the minimum amount of noise to be added for
decorrelation.
