Equiangular lines, projective symmetries and nice error frames
Year: 2015
Type: dissertation
Abstract: The existence of maximal sets of equiangular lines (SIC-POVMs) is of interest to the mathematics and physics communities due to their connection to quantum information theory, quantum cryptography, spherical 2-designs and cubature rules. This thesis looks at a way to recover analytic SIC-POVMs from numerical SIC-POVMs, including the discovery of a new analytic SIC-POVM in 17 dimensions. It also develops a way to comprehensively find nice error bases (used for finding SIC-POVMs). Finally, a general theory to classify sequences of vectors up to projective unitary equivalence is developed and applied to study the projective symmetry groups of sequences of vectors.
Author: Tuan-Yow Chien
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2617033736