  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.
