New approach to Epsilon-entropy and Its comparison with Kolmogorov's   Epsilon-entropy
  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. 
Kei Inoue, Takashi Matsuoka and Masanori Ohya