Date of Award

8-2023

Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)

Department

Physics, Applied

First Advisor

Christopher Fuchs

Second Advisor

Olga Goulko

Third Advisor

Marcus Appleby

Abstract

In this work, we use numerical techniques to investigate a conjecture first posited in \cite{sicNumerics} to do with the structure of quantum mechanics. Particularly, we investigate a mathematical property of objects known as symmetric informationally complete positive operator valued measures (SIC POVMs), which are especially important to QBism. SIC POVMs, when they exist, may be used to represent quantum states in a unique way, and their many beautiful symmetries have been noticed in a number of subfields of mathematics and in quantum information theory. The conjecture at its most basic concerns whether we can use the symmetries of these objects to reduce the complexity of searching for them. In general, to search for these objects we need to solve $d^{2}$ simultaneous 4th-order equations, where d is the dimension of the vector space. However, if the conjecture is true, we would only need to solve about 3$d$/2 of them. The numerical results imply that the conjecture is true, dropping the complexity of searching for SICs from a quadratic to a linear number of equations in $d$. Here we take a quantum information theory perspective for how these objects are discussed.

Comments

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