  In this paper, we study the decoherence property of synchronization master
equation for networks of qubits interconnected by swapping operators. The
network Hamiltonian is assumed to be diagonal with different entries so that it
might not be commutative with the swapping operators. We prove a theorem
establishing a general condition under which almost complete decohernece is
achieved, i.e., all but two of the off-diagonal entries of the network density
operator asymptotically tend to zero. This result explicitly shows that quantum
dissipation networks tend to forget the information initially encoded when the
internal (induced by network Hamiltonian) and external (induced by swapping
operators) qubit interactions do not comply with each other.
