We consider a family of quantum channels characterized by the fact that certain (in general nonorthogonal) Pure states at the channel entrance are mapped to (tensor) Products of Pure states (PPP, hence pcubed) at the complementary outputs (the main output and the environment) of the channel. The pcubed construction, a reformulation of the twisted-diagonal procedure by M. M Wolf and D. Perez-Garcia, [Phys. Rev. A 75, 012303 (2007)], can be used to produce a large class of degradable quantum channels; degradable channels are of interest because their quantum capacities are easy to calculate. Several known types of degradable channels are either pcubed channels, or subchannels (employing a subspace of the channel entrance), or continuous limits of pcubed channels. The pcubed construction also yields channels which are neither degradable nor antidegradable (i.e., the complement of a degradable channel); a particular example of a qutrit channel of this type is studied in some detail. Determining whether a pcubed channel is degradable or antidegradable or neither is quite straightforward given the pure input and output states that characterize the channel. Conjugate degradable pcubed channels are always degradable.
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