  The time evolution of a qubit, consisting of two single-level quantum dots,
is studied in the presence of telegraph noise. The dots are connected by two
tunneling paths, with an Aharonov-Bohm flux enclosed between them. Under
special symmetry conditions, which can be achieved by tuning gate voltages,
there develops partial decoherence: at long times, the off-diagonal element of
the reduced density matrix (in the basis of the two dot states) approaches a
non-zero value, generating a circulating current around the loop. The flux
dependence of this current contains full information on the initial quantum
state of the qubit, even at infinite time. Small deviations from this symmetry
yield a very slow exponential decay towards the fully-decoherent limit.
However, the amplitudes of this decay also contain the full information on the
initial qubit state, measurable either via the current or via the occupations
of the qubit dots.
