Fashioning Classical Stochastic Processes Via Quantum Noises
The advancements in quantum technologies afford the possibilities to exploit the inherent probabilistic nature of quantum processes for creating and manipulating classical stochastic processes in novel ways. We will consider quantum version of semigroups that are Markovian and characterize their asymptotic behavior using the tools of quantum probability. After looking at few quantum optical circuits to motivate the study, we will focus on construction of *-homomorphisms on IRR of compact groups as a consequence of Peter-Weyl theorem. The evolutions are fashioned on a space that is a Plancherel decomposition of a compact group satisfying the axiom of second countability and look at specific examples. Finally, we will outline open problems in obtaining the limits of evolutions with non-classical initial states for some groups of interest in quantum physics.