  In this article we study lossless compression of strings of pure quantum
states of indeterminate-length quantum codes which were introduced by
Schumacher and Westmoreland. Past work has assumed that the strings of quantum
data are prepared to be encoded in an independent and identically distributed
way. We introduce the notion of quantum stochastic ensembles, allowing us to
consider strings of quantum states prepared in a more general way. For any
identically distributed quantum stochastic ensemble we define an associated
quantum Markov chain and prove that the optimal average codeword length via
lossless coding is equal to the quantum dynamical entropy of the associated
quantum Markov chain.
