Faculty Advisor

Aravind, Padmanabhan K.

Faculty Advisor

Martin, William J.

Abstract

The purpose of this project is first to survey all known simple constructions of SIC-POVMs and second to explore these solutions for additional symmetries. We focus on three main constructions: the Weyl-Heisenberg construction; constructions using Hadamard matrices; and Hoggar's construction. We then explore fiducial vectors in dimensions 7 and 19 which have additional attractive number-theoretic properties. Finally, we generate geometric configurations of the Majorana states of some SIC-POVMs in dimensions 3 and 4. We then plot the Majorana vectors of those SIC-POVMs in real dimension 3; these are then found to have special symmetry. In the process of generating the Majorana states, two potentially new SIC-POVMs in dimension three have been found.

Publisher

Worcester Polytechnic Institute

Date Accepted

April 2017

Major

Physics

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Physics

Advisor Department

Mathematical Sciences

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