Chapter 7 - Dynamic quantum Bernoulli random walks

Abstract

Quantum probability is a very active research area motivated by applications in physics, information theory, and biology. This chapter illustrates dynamic quantum Bernoulli random walks. The chapter also introduces some notions of quantum probability. Bernoulli random walks can be realized on a space called the dual of SU (2). It is just the set of natural numbers equipped with some non-commutative law. The model of dynamic random walks on the dual of SU (2) focuses on some limit theorems like local limit theorem and central limit theorem. The local limit and central theorems provides a large deviation principle and can give a characterization of a large class of transient dynamic random walks. A classical random variable over a probability space taking values in a measurable space can gives rise to a quantum random variable. It has been proved that Quantum Bernoulli Random Walks (QBRW) can be related to a random walk of the dual of SU (2). The dynamic random walk on the dual of SU (2) can be defined as the Markov chain.