|
| related topics |
| {information, entropy, channel} |
| {let, theorem, proof} |
| {classical, space, random} |
| {energy, gaussian, time} |
| {observables, space, algebra} |
| {algorithm, log, probability} |
|
New approach to Epsilon-entropy and Its comparison with Kolmogorov's
Epsilon-entropy
Kei Inoue, Takashi Matsuoka, Masanori Ohya
abstract: Kolmogorov introduced a concept of Epsilon-entropy to analyze information in
classical continuous system. The fractal dimension of geometrical sets was
introduced by Mandelbrot as a new criterion to analyze the complexity of these
sets. The Epsilon-entropy and the fractal dimension of a state in general
quantum system were introduced by one of the present authors in order to
characterize chaotic properties of general states.
In this paper, we show that Epsilon-entropy of a state includes Kolmogorov
Epsilon-entropy, and the fractal dimension of a state describe fractal
structure of Gaussian measures.
- oai_identifier:
- oai:arXiv.org:quant-ph/9806027
- categories:
- quant-ph
- comments:
- 17 pages, Latex, Submitted to Journal of Mathematical Physics
- arxiv_id:
- quant-ph/9806027
- created:
- 1998-06-08
- updated:
- 1998-06-12
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