Average mutual information of the random block-message ensembles for many-letters

By making use of the theoretical framework presented by Bostroem (K. J. Bostroem, LANL quant-ph/0009052), we generalize the standard quantum information theory of block messages with fixed block length to the variable one. We show that the states belonging to a sufficiently large Hilbert space are the highly distinguishable states. We also consider the collection states (product states of more than one qubit state) and seek a "pretty good measurement"(PGM) with measurement vectors to improve the mutual information. The average mutual information over random block-message ensembles with variable block length n is discussed in detail.