  We consider the important class of quantum operations (completely positive
trace-preserving maps) called entanglement breaking channels. We show how every
such channel induces stochastic matrix representations that have the same
non-zero spectrum as the channel. We then use this to investigate when
entanglement breaking channels are primitive, and prove this depends on
primitivity of the matrix representations. This in turn leads to tight bounds
on the primitivity index of entanglement breaking channels in terms of the
primitivity index of the associated stochastic matrices. We also present
examples and discuss open problems generated by the work.
