  We investigate the decoherence process for a quantum register composed of N
qubits coupled to an environment. We consider an environment composed of one
common phonon bath and several electronic baths. This environment is relevant
to the implementation of a charge based solid-state quantum computer. We
explicitly compute the time evolution of all off-diagonal terms of the
register's reduced density matrix. We find that in realistic configurations,
"superdecoherence" and "decoherence free subspaces" do not exist for an N-qubit
system. This means that all off-diagonal terms decay like exp(-q(t)N), where
q(t) is of the same order as the decay function of a single qubit.
