  We consider noisy, non-local unitary operations or interactions, i.e. the
corresponding evolutions are described by completely positive maps or master
equations of Lindblad form. We show that by random local operations the
completely positive maps can be depolarized to a standard form with a reduced
number of parameters describing the noise process in such a way that the
noiseless (unitary) part of the evolution is not altered. A further reduction
of the parameters, in many cases even to a single one (i.e. global white
noise), is possible by tailoring the decoherence process and increasing the
amount of noise. We generalize these results to the dynamical case where the
ideal unitary operation is given by some interaction Hamiltonian. The resulting
standard forms may be used to compute lower bounds on channel capacities, to
simplify quantum process tomography or to derive error thresholds for
entanglement purification and quantum computation.
