  In this paper, using the notion of nonlinear coherent states, we define a
deformed bosonic dephasing channel modelling the impact of a Kerr medium on a
quantum state, as it occurs, for instance, in quantum communication based on
optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able
to compensate the dephasing. In addition, our studies reveal that the quantum
capacity of the deformed bosonic dephasing channel can be greater than that of
the undeformed, standard bosonic dephasing channel for certain nonlinearity
parameters.
