Faculty Advisor or Committee Member

P.K. Aravind, Advisor

Faculty Advisor or Committee Member

Alex Zozulya, Committee Member

Faculty Advisor or Committee Member

Alex Zozulya

Identifier

etd-042816-121320

Abstract

The objective of this thesis is to use the Majorana description of a spin-1 system to give a geometrical construction of a maximal set of Mutually Unbiased Bases (MUBs) and Symmetric Informationally Complete Positive Operator Valued Measures (SIC-POVMs) for this system. In the Majorana Approach, an arbitrary pure state of a spin-1 system is represented by a pair of points on the Reimann sphere, or a pair of unit vectors (known as Majorana vectors or M-vectors). Spin-1 states can be of three types: those whose vectors are parallel, those whose vectors are antiparallel and those whose vectors make an arbitrary angle. The types of bases possible for a spin-1 system are thus geometrically much more varied than for a spin-half system or qubit, which is the standard unit of information storage in most quantum protocols. Our derivation of the MUBs and SIC-POVMs proceeds from a recently derived expression for the squared overlap of two spin-1 states in terms of their M-vectors and the minimal additional set of assumptions that are needed. These assumptions include time-reversal invariance in the case of the MUBs and the requirement of three-fold symmetry in the case of the SIC-POVMs. The applications of these results to problems in quantum information are mentioned.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Physics

Project Type

Thesis

Date Accepted

2016-04-28

Accessibility

Restricted-WPI community only

Subjects

Quantum Protocols, SIC-POVMs, MUBs, Geometrical Construction, Majorana Representation

Available for download on Tuesday, April 28, 2020

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