  We describe a method for lossless quantum compression if the output of the
information source is not known. We compute the best possible compression rate,
minimizing the expected base length of the output quantum bit string (the base
length of a quantum string is the maximal length in the superposition). This
complements work by Schumacher and Westmoreland who calculated the
corresponding rate for minimizing the output's average length.
  Our compressed code words are prefix-free indeterminate-length quantum bit
strings which can be concatenated in the case of multiple sources. Therefore,
we generalize the known theory of prefix-free quantum codes to the case of
strings with indeterminate length. Moreover, we describe a communication model
which allows the lossless transmission of the compressed code words. The
benefit of compression is then the reduction of transmission errors in the
presence of noise.
