Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy

Abstract

We describe some basic results for Quantum Stochastic Processes and present some new results about a certain class of processes which are associated to Quantum Iterated Function Systems (QIFS). We discuss questions related to the Markov property and we present a definition of entropy which is induced by a QIFS. This definition is a natural generalization of the Shannon-Kolmogorov entropy from Ergodic Theory. This definition is different from the one in the paper "A Thermodynamic Formalism for density matrices in Quantum Information" by the same authors.