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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Le, Junjiang

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042717-092112

Advisor

• Martin, William J.
• Aravind, Padmanabhan K.

Year

• 2017

Date created

• 2017-04-27

Resource type

• Major Qualifying Project

Major

• Interdisciplinary

Rights statement

• In Copyright

License

• All rights reserved