  We have in mind a register of qubits for an quantum information system, and
consider its decoherence in an idealized but typical situation. Spontaneous
decay and other couplings to the far environment considered as the world
outside the quantum apparatus will be neglected, while couplings to quantum
states within the apparatus, i.e. to a near environment are assumed to
dominate. Thus the central system couples to the near environment which in turn
couples to a far environment. Considering that the dynamics in the near
environment is not sufficiently well known or controllable, we shall use random
matrix methods to obtain analytic results. We consider a simplified situation
where the central system suffers weak dephasing from the near environment,
which in turn is coupled randomly to the far environment. We find the
anti-intuitive result that increasing the coupling between near and far
environment actually protects the central qubit.
