Physical Sciences and Mathematics Commons^™

Studies Of Small Systems In Quantum Information, Sai Vinjanampathy

LSU Doctoral Dissertations

I study two topics in quantum information theory from the perspective of algebra and geometry. The first relates to exploring the geometry of unitary operators for small quantum systems, specifically three-level systems. Such an understanding of the space over which quantum systems evolve is central to understanding the detailed dynamics of quantum systems and to understand the correlation properties of subsystems that compose a given quantum system. The geometry of unitary operators also allows for the calculation of path-dependent phases called geometric phases. These geometric phases are central to understanding a variety of experiments. I present a general technique, called …