  We analyze the ultimate quantum limit on the accessible information for an
optical communication scheme when time bins carry coherent light pulses
prepared in one of several orthogonal modes and the phase undergoes diffusion
after each channel use. This scheme, an example of a quantum memory channel,
can be viewed as noisy pulse position modulation (PPM) keying with phase
fluctuations occurring between consecutive PPM symbols. We derive a general
expression for the output states in the Fock basis and implement a numerical
procedure to calculate the Holevo quantity. Using asymptotic properties of
Toeplitz matrices, we also present an analytic expression for the Holevo
quantity valid for very weak signals and sufficiently strong dephasing when the
dominant contribution comes from the single-photon sector in the Hilbert space
of signal states. Based on numerical results we conjecture an inequality for
contributions to the Holevo quantity from multiphoton sectors which implies
that in the asymptotic limit of weak signals, for arbitrarily small dephasing
the accessible information scales linearly with the average number of photons
contained in the pulse. Such behaviour presents a qualitative departure from
the fully coherent case.
