Higher linear algebra in topology and quantum information theory

Thesis

We investigate categorifications of linear algebra, and their applications to the construction of 4-manifold invariants, to the construction of a variety of linear algebraic structures in quantum information theory, and to the classification of certain instances of `quantum pseudo-telepathy', a phenomenon in quantum physics where two non-communicating parties can use pre-shared entanglement to perform tasks classically impossible without communicating.

This thesis is divided into f...

Expand abstract

Authors: Reutter, D

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: quantum graph isomorphism; monoidal 2-category; group of central type; biunitary; noncommutative graph; quantum pseudo-telepathy; 4-manifold invariant; unitary error basis; state-sum; topological field theory; graphical calculus; quantum information; categorification; fusion category
• Subjects: Category Theory; Quantum Algebra