  Quantum entanglement can be studied through the theory of completely positive
maps in a number of ways, including by making use of the Choi-Jamilkowski
isomorphism, which identifies separable states with entanglement breaking
quantum channels, and optimal ensemble length with entanglement breaking rank.
The multiplicative domain is an important operator structure in the theory of
completely positive maps. We introduce a new technique to determine if a
channel is entanglement breaking and to evaluate entanglement breaking rank,
based on an analysis of multiplicative domains determined by complementary
quantum channels. We give a full description of the class of entanglement
breaking channels that have a projection as their Choi matrix, and we show the
entanglement breaking and Choi ranks of such channels are equal.
