On Lossless Quantum Data Compression and Quan- tum Variable–Length Codes

In Shannon’s Foundation of Information Theory ([27]) perhaps the most basic contributions are Source Coding Theorems (lossy and lossless) and the Channel Coding Theorem. In the most natural and simple source model DMS the source outputs a sequence X1, X2, . . . of independent, identically distributed random variables taking finitely many values. The Lossy Source Coding Theorem says that this sequence can be compresed by block coding with arbitrarily small error probability at a rate H(P ), the entropy of the common distribution P of the Xi’s. (Later Shannon gave an extension replacing the probability of error criterion by general fidelity criteria and an ingenious formula for the rate–distortion function replacing H(P ).)