New approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy

Inoue, Kei; Matsuoka, Takashi; Ohya, Masanori

New approach to Epsilon-entropy and Its comparison with Kolmogorov's Epsilon-entropy

Authors

Inoue, Kei

Matsuoka, Takashi

Ohya, Masanori

Description

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.
17 pages, Latex, Submitted to Journal of Mathematical Physics