  We identify and discuss nonlinear phase noise arising in Kerr self-phase
modulation of a coherent light pulse propagating through an attenuating medium
with third-order nonlinearity in a dispersion-free setting. This phenomenon,
accompanying the standard unitary Kerr transformation of the optical field, is
described with high accuracy as Gaussian phase diffusion with parameters given
by closed expressions in terms of the system properties. We show that the
irreversibility of the nonlinear phase noise ultimately limits the ability to
transmit classical information in the phase variable over a lossy single-mode
bosonic channel with Kerr-type nonlinearity. Our model can be also used to
estimate the amount of squeezing attainable through self- phase modulation in a
Kerr medium with distributed attenuation.
