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arXiv quant-ph/96120431996-12quant-ph

Asymptotic Redundancies for Universal Quantum Coding

Christian Krattenthaler, Paul Slater

备注：: 35 pages, AmS-LaTeX v1.2, with psfig.sty, two postscript figures (fig2.eps, fig3.eps). This is a substantial revision of the previous version. The introduction was rewritten completely. The minimax redundancy problem is now resolved as well
发表信息：: IEEE Trans.Info.Theor. 46 (2000) 801-819

英文摘要：

We investigate the question of whether or not there exists a noncommutative/ quantum extension of a recent (commutative probabilistic) result of Clarke and Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy - the excess of the encoding cost over the source entropy - of universal data compression in a parametric setting. We study certain probability distributions for the two-level quantum systems. We are able to compute exact formulas for the corresponding redundancies, for which we find the asymptotic limits. These results are very suggestive and do indeed point towards a possible quantum extension of the result of Clarke and Barron.

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