Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy

TL;DR

This paper explores quantum stochastic processes and introduces a new entropy concept linked to Quantum Iterated Function Systems, extending classical entropy ideas to quantum settings.

Contribution

It presents new results on quantum processes associated with QIFS and proposes a novel entropy definition generalizing Shannon-Kolmogorov entropy.

Findings

New results on quantum processes related to QIFS

A natural generalization of classical entropy to quantum systems

Discussion on the Markov property in quantum contexts

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.