Date & Time: Wednesday, July 30, 2008, 16:00-17:00.
Venue: Ramanujan Hall
Title: Possible Links Between Physics Problems in Quantum Computing and Fibre Bundles, Projective Geometry and Coding/Design Theory
Speaker: Ravi. P. Rau, Louisiana State University
Abstract: Quantum Information, the field that embraces quantum computing, cryptography and teleportation, involves as a central object an entangled pair of spin-1/2 (or two-level) systems. I have been interested in developing geometrical pictures for manipulating the fifteen-operator su(4) algebra that describes such systems. For a single spin, its su(2) algebra's fibre bundle of a two-sphere (called Bloch sphere by physicists) and a u(1) phase plays a major role throughout the field of magnetic resonance. I will present analogous geometrical descriptions of fibre bundles for su(4) and its sub-algebras. One of these sub-algebras, su(2) x su(2) x u(1), also "maps" onto octonions and the Fano Plane. Other sub-algebras and the full su(4) can be similarly related to Desargues's and other diagrams of projective geometry. Interestingly, these relate to the subjects of coding and design theory, the latter having been called "a mathematical theory born in British India", actually Bombay!