  We study a model of dephasing (decoherence) in a two-state quantum system
(qubit) coupled to a bath of harmonic oscillators. An exact analytic solution
for the reduced dynamics of a two-state system in this model has been obtained
previously for factorizing initial states of the combined system. We show that
the model admits exact solutions for a large class of correlated initial states
which are typical in the theory of quantum measurements. We derive exact
expressions for the off-diagonal elements of the qubit density matrix, which
hold for an arbitrary strength of coupling between the qubit and the bath. The
influence of initial correlations on decoherence is considered for different
bath spectral densities. Time behavior of the qubit entropy in the decoherence
process is discussed.
