Non-commutative probability : from classical to quantum probability

Abstract

In classical probability theory, it is implicitly assumed that random variables commute. However, this assumption does not necessarily hold in all mathemat ical frameworks, such as those involving matrices. In this thesis, we will explore quantum probability, a non-commutative extension of classical probability. The main aim of this thesis shall be to examine how key concepts from classical probability can be generalized in the quantum setting.