We show that measurements of finite duration performed on an open two-state
system can protect the initial state from a phase-noisy environment, provided
the measured observable does not commute with the perturbing interaction. When
the measured observable commutes with the environmental interaction, the
finite-duration measurement accelerates the rate of decoherence induced by the
phase noise. For the description of the measurement of an observable that is
incompatible with the interaction between system and environment, we have found
an approximate analytical expression, valid at zero temperature and weak
coupling with the measuring device. We have tested the validity of the
analytical predictions against an exact numerical approach, based on the
superoperator-splitting method, that confirms the protection of the initial
state of the system. When the coupling between the system and the measuring
apparatus increases beyond the range of validity of the analytical
approximation, the initial state is still protected by the finite-time
measurement, according with the exact numerical calculations.Comment: REVISED VERSION: 37 pages, 3 figure