  It is commonly stated that decoherence in open quantum systems is due to
growing entanglement with an environment. In practice, however, surprisingly
often decoherence may equally well be described by random unitary dynamics
without invoking a quantum environment at all. For a single qubit, for
instance, pure decoherence (or phase damping) is always of random unitary type.
Here, we construct a simple example of true quantum decoherence of two qubits:
we present a feasible phase damping channel of which we show that it cannot be
understood in terms of random unitary dynamics. We give a very intuitive
geometrical measure for the positive distance of our channel to the convex set
of random unitary channels and find remarkable agreement with the so-called
Birkhoff defect based on the norm of complete boundedness.
