On lossless quantum data compression with a classical helper

Ahlswede R, Cai N (2004)
IEEE TRANSACTIONS ON INFORMATION THEORY 50(6): 1208-1219.

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After K. Bostrom and T. Felbinger observed that lossless quantum data compression does not exist unless decoders know the lengths of codewords, they introduced a classical noiseless channel to inform the decoder of a quantum source about the lengths of codewords. In this paper we analyze their codes and present 1) a sufficient and necessary condition for the existence of such codes for given lists of lengths of codes; 2) a characterization of the optimal compression rate for their codes. However our main contribution is a more efficient way to use the classical channel. We propose a more general coding scheme. It turned out that the optimal compression can always be achieved by a code obtained by this scheme. A von Neumann entropy lower bound to rates of our codes and a necessary and sufficient condition to achieve the bound are obtained. The gap between this lower bound and the compression rates is also well analyzed. For a special family of quantum sources we provide a sharper lower bound in terms of Shannon entropy. Finally, we propose some problems for further research.
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Ahlswede R, Cai N. On lossless quantum data compression with a classical helper. IEEE TRANSACTIONS ON INFORMATION THEORY. 2004;50(6):1208-1219.
Ahlswede, R., & Cai, N. (2004). On lossless quantum data compression with a classical helper. IEEE TRANSACTIONS ON INFORMATION THEORY, 50(6), 1208-1219. doi:10.1109/TIT.2004.828071
Ahlswede, R., and Cai, N. (2004). On lossless quantum data compression with a classical helper. IEEE TRANSACTIONS ON INFORMATION THEORY 50, 1208-1219.
Ahlswede, R., & Cai, N., 2004. On lossless quantum data compression with a classical helper. IEEE TRANSACTIONS ON INFORMATION THEORY, 50(6), p 1208-1219.
R. Ahlswede and N. Cai, “On lossless quantum data compression with a classical helper”, IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 50, 2004, pp. 1208-1219.
Ahlswede, R., Cai, N.: On lossless quantum data compression with a classical helper. IEEE TRANSACTIONS ON INFORMATION THEORY. 50, 1208-1219 (2004).
Ahlswede, Rudolf, and Cai, N. “On lossless quantum data compression with a classical helper”. IEEE TRANSACTIONS ON INFORMATION THEORY 50.6 (2004): 1208-1219.
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