A quantum analog of Huffman coding

We construct a Huffman-coding inspired scheme for quantum data compression. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be polynomial in log N by a massively parallel implementation of a quantum gate array. This is to be compared with the O(N³) computational steps required in the sequential implementation by Cleve and Di-Vincenzo (see Phys. Rev. A54, p.2636, 1996) of the Schumacher (see Phys. Rev. A51, p.2738, 1995) quantum noiseless block coding scheme