Noncommutative Probability Models in Quantum Communication and Multi-Agent Stochastic Control

In this paper, we present a survey of basic results in quantum communication theory that utilize heavily so-called noncommutative probability models. We indicate by means of examples how these mathematical methods can lead to actual computations in specific examples. We offer a careful review of these non-commutative models and we observe the similarities with desired features in the representation of the statistics in multi-agent stochastic control problems. We then give suggestions for integrating some of the basic constructs of quantum models in the language of multi-agent stochastic control systems.