  The quantum capacity of a quantum channel captures its capability for
noiseless quantum communication. It lies at the heart of quantum information
theory. Unfortunately, our poor understanding of nonadditivity of coherent
information makes it hard to understand the quantum capacity of all but very
special channels. In this paper, we consider the dephrasure channel, which is
the concatenation of a dephasing channel and an erasure channel. This very
simple channel displays remarkably rich and exotic properties: we find
nonadditivity of coherent information at the two-letter level, a big gap
between single-letter coherent and private informations, and positive quantum
capacity for all complementary channels. Its clean form simplifies the
evaluation of coherent information substantially and, as such, we hope that the
dephrasure channel will provide a much-needed laboratory for the testing of new
ideas about nonadditivity.
