On quantum coding for ensembles of mixed states
  We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem. 
Howard Barnum, Carlton M. Caves, Christopher A. Fuchs, Richard Jozsa   and Benjamin W. Schumacher