  A qubit (containing two quantum states, 1 and 2), is coupled to a control
register (state 3), which is subject to telegraph noise. We study the time
evolution of the density matrix $\rho$ of an electron which starts in some
coherent state on the qubit. At infinite time, $\rho$ usually approaches the
fully decoherent state, with $\rho^{}_{nm}=\delta^{}_{nm}/3$. However, when the
Hamiltonian is symmetric under $1\leftrightarrow 2$, the element $\rho^{}_{12}$
approaches a non-zero real value, implying a partial coherence of the
asymptotic state. The asymptotic density matrix depends only on ${\rm
Re}[\rho^{}_{12}(t=0)]$. In several cases, the information stored on the qubit
is protected from the noise.
