Isoclinic Subspaces and Quantum Error Correction

Date

2020-04-15

Authors

Mammarella, David

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Publisher

University of Guelph

Abstract

This thesis studies the classical notion of canonical angles to explore isoclinic subspaces on a complex inner product space and equivalent conditions are developed for a set of subspaces to be isoclinic. A connection between isoclinic subspaces and quantum error correction will be identified. We will show that every quantum error correcting code is associated with a family of isoclinic subspaces and a partial converse for pairs of such subspaces will be proved. It will also be shown how the canonical angles for isoclinic subspaces arise in the structure of the higher rank numerical ranges of the corresponding orthogonal projections. An examination of how this connection could be used to fuel other ideas in quantum error correction and quantum information theory in general will be discussed to conclude this work.

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Keywords

Quantum information, Quantum Error Correction, Linear Algebra, Operator Theory

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