Physics & Astronomy - Virtual PhD Thesis Defense - William Braasch, Dartmouth
Title: "Aspects of Quantum Dynamics in Phase Space"
Abstract: The Wigner function has proved to be a useful representation of quantum states in phase space where comparisons between classical and quantum mechanics are readily made. Performing such comparisons has become a practical issue in fields such as quantum computing. Specification of the difference between the two theories can enable researchers to identify where and how quantum protocols may outperform their classical counterparts. In this talk, I describe our contributions towards understanding quantum dynamics in phase space with a focus on discrete-variable quantum systems. Quantum states for such systems are represented with a discrete Wigner function in phase space consisting of an array of points with toroidal boundary conditions and a measure of area. I will show how the peculiar feature of negative transition quasiprobabilities between discrete phase space points arises. Furthermore, I will draw a comparison with classical probabilistic processes, explore the properties of these transition quasiprobabilities, and investigate their geometrical constraints.