New approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy
Quantum Physics
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.quant-ph/9806027,
title = {New approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy},
author = {Kei Inoue and Takashi Matsuoka and Masanori Ohya},
journal= {arXiv preprint arXiv:quant-ph/9806027},
year = {2007}
}
Comments
17 pages, Latex, Submitted to Journal of Mathematical Physics