dorsal/arxiv
View SchemaNew approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy
| Authors | Kei Inoue, Takashi Matsuoka, Masanori Ohya |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806027 |
| URL | https://arxiv.org/abs/quant-ph/9806027 |
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.
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"abstract": "Kolmogorov introduced a concept of Epsilon-entropy to analyze information in\nclassical continuous system. The fractal dimension of geometrical sets was\nintroduced by Mandelbrot as a new criterion to analyze the complexity of these\nsets. The Epsilon-entropy and the fractal dimension of a state in general\nquantum system were introduced by one of the present authors in order to\ncharacterize chaotic properties of general states.\n In this paper, we show that Epsilon-entropy of a state includes Kolmogorov\nEpsilon-entropy, and the fractal dimension of a state describe fractal\nstructure of Gaussian measures.",
"arxiv_id": "quant-ph/9806027",
"authors": [
"Kei Inoue",
"Takashi Matsuoka",
"Masanori Ohya"
],
"categories": [
"quant-ph"
],
"title": "New approach to Epsilon-entropy and Its comparison with Kolmogorov\u0027s Epsilon-entropy",
"url": "https://arxiv.org/abs/quant-ph/9806027"
},
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