Title: Classical and Quantum Factors of Channels,
Abstract: Given a classical channel, a stochastic map from inputs to outputs, can we
replace the input with a simple intermediate variable that still yields the
correct conditional output distribution? We examine two cases: first, when the
intermediate variable is classical; second, when the intermediate variable is
quantum. We show that the quantum variable's size is generically smaller than
the classical, according to two different measures---cardinality and entropy.
We demonstrate optimality conditions for a special case. We end with several
related results: a proposal for extending the special case, a demonstration of
the impact of quantum phases, and a case study concerning pure versus mixed
states.