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

Optimality in Quantum Data Compression using Dynamical Entropy