Data Compression for Quantum Code

The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first perform classical data compression before performing the quantum data compression for individual subspaces. For minimizing the resource in quantum coding, a general parameterization of the dimensions in the Jozsa-Schumacher quantum data compression scheme is presented.