On lossless quantum data compression with a classical helper
After K. Bostro/spl uml/m 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 th...
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| Veröffentlicht in: | IEEE transactions on information theory 2004-06, Vol.50 (6), p.1208-1219 |
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| creator | Ahlswede, R. Ning Cai |
| description | After K. Bostro/spl uml/m 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. |
| doi_str_mv | 10.1109/TIT.2004.828071 |
| format | Article |
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Bostro/spl uml/m 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.</description><subject>Channels</subject><subject>Compressing</subject><subject>Data compression</subject><subject>Decoders</subject><subject>Decoding</subject><subject>Entropy</subject><subject>Hilbert space</subject><subject>Information theory</subject><subject>Length measurement</subject><subject>Lossless</subject><subject>Lower bounds</subject><subject>Mathematics</subject><subject>Optimization</subject><subject>Performance evaluation</subject><subject>Quantum mechanics</subject><subject>Quantum theory</subject><subject>Sufficient conditions</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kEtLxDAURoMoOI6uXbgJLsRNZ_JsEnAjg4-Bgdl0H9I0ZTqkD5MW8d-boYLgwtXlu5zvwj0A3GK0whipdbEtVgQhtpJEIoHPwAJzLjKVc3YOFghhmSnG5CW4ivGYIuOYLMDTvoO-j9G7GOHHZLpxamFlRgNt3w4hbZu-g5_NeIBp5U3K1nh4cH5w4Rpc1MZHd_Mzl6B4fSk279lu_7bdPO8ySxUeM14aUZWS1U6SsrKU1IYLZSUWLq8Er5UQ3FZCUpTzOre4lNSgmlnJRYVyQZfgYT47hP5jcnHUbROt8950rp-iJpJhohBL4OO_IM7FCaScJPT-D3rsp9ClLzRWXCqmGE7QeoZsSIqCq_UQmtaEL42RPknXSbo-Sdez9NS4mxuNc-6XpogQpeg3Wk98LQ</recordid><startdate>20040601</startdate><enddate>20040601</enddate><creator>Ahlswede, R.</creator><creator>Ning Cai</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Bostro/spl uml/m 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. 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| source | IEEE Electronic Library (IEL) |
| subjects | Channels Compressing Data compression Decoders Decoding Entropy Hilbert space Information theory Length measurement Lossless Lower bounds Mathematics Optimization Performance evaluation Quantum mechanics Quantum theory Sufficient conditions |
| title | On lossless quantum data compression with a classical helper |
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