  We study the possibility of discriminating between two bosonic dephasing
quantum channels. We show that unambiguous discrimination is not realizable. We
then consider discrimination with nonzero error probability and minimize this
latter in the absence of input constraints. In the presence of an input energy
constraint, we derive an upper bound on the error probability. Finally, we
extend these results from single-shot to multi-shot discrimination, envisaging
the asymptotic behavior.
