  We consider visible compression for discrete memoryless sources of mixed
quantum states when only classical information can be sent from Alice to Bob.
We assume that Bob knows the source statistics, and that Alice and Bob have
identical random number generators. We put in an information theoretic
framework some recent results on visible compression for sources of states with
commuting density operators, and remove the commutativity requirement. We
derive a general achievable compression rate, which is for the noncommutative
case still higher than the known lower bound. We also present several related
problems of classical information theory, and show how they can be used to
answer some questions of the mixed state compression problem.
