  Dephasing is a prominent noise mechanism that afflicts quantum information
carriers, and it is one of the main challenges towards realizing useful quantum
computation, communication, and sensing. Here we consider discrimination and
estimation of bosonic dephasing channels, when using the most general adaptive
strategies allowed by quantum mechanics. We reduce these difficult quantum
problems to simple classical ones based on the probability densities defining
the bosonic dephasing channels. By doing so, we rigorously establish the
optimal performance of various distinguishability and estimation tasks and
construct explicit strategies to achieve this performance. To the best of our
knowledge, this is the first example of a non-Gaussian bosonic channel for
which there are exact solutions for these tasks.
