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|TOWARDS QUANTUM e—ENTROPY AND VALIDITY OF QUANTUM |
INFORMATION V. P. Belavkin Department of Mathematics University of
Nottingham Nottingham NG7 2RD, UK The Bayesian method in quantum signal
processing was ...
|StÝrmer, E.: Entropy of some automorphisms of the II1-factor of the free group in |
infinite number of generators. Invent. Math., 110, 63–73 (1992). 207. StÝrmer, E.:
Entropy of some inner automorphisms of the hyperfinite II1-factor. Internat.
|Golodets, V. Ya. and StÝrmer, E. Entropy of C*-dynamical systems defined by |
bitstreams, Ergod. Th. & Dynam. Sys. 18 (1998), 859–874. Golodets, V. Ya. and
StÝrmer, E. Generators and comparison of entropies of automorphisms of finite
|e-ENTROPY of a set in a metric space - The logarithm to the base 2 of the |
smallest number of points in an e-net for this set. In other words, the e-entropy 3%
.(C, X) of a set Clying in a metric space (X, p) is 3%.(C, X) - log2N.(C, X), where l
|If the smallest number of the convex sets needed to cover the set F is N (e), then |
we call the dimension given by . ,_ .. log N (e) dc F = hm t— — - e-M> log (1/e) the
capacity dimension (or the e-entropy dimension) of the set F. These two fractal ...
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|The entropy of any infinite source equals infinity. We feel that an element of a |
square carries more information then an element of a segment. However, their
entropies are equal. We are going next to introduce the concept of e-entropy.
|The fact that the conditional measures on the elements of E are proportional to |
the restrictions /I6i to these elements, together ... It follows from Lemma 5.2 that
there exists 6(e) > 0 such that if max(diamQ, diamP, t) < 6(e), then the e-entropy
of V ...
|In other words, if one computes the information production rate as a function of e, |
say h(e), then it will equal to hks for all e < eo. For a chaotic “flow”, with many
active degrees of freedom, this Kolmogorov-Sinai entropy is infinite. In such a