Asymptotic Redundancies for Universal Quantum Coding

Details Asymptotic Redundancies for Universal Quantum Coding Asymptotic Redundancies for Universal Quantum Coding

1996-12-18

arxiv.org/abs/quant-ph/9612043v3

IEEE Trans.Info.Theor. 46 (2000) 801-819

Physics

Quantum Physics

35 pages, AmS-LaTeX v1.2, with psfig.sty, two postscript figures (fig2.eps, fig3.eps). This is a substantial revision of the p

Scientific paper

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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