From Möbius Strips to Twisted Toric Codes: A Homological Approach to Quantum Low Density Parity Check Codes

In the past few years, the search for good quantum low density parity check (qLDPC) codes suddenly took flight, and many different constructions of these codes have since been presented, including many product constructions. As these code constructions have a natural interpretation in the language of homology, this thesis studies the interplay...

Inequalities and Quantum Entanglement: From the Cauchy-Schwarz Inequality to Non-linear Entanglement Witnesses

In this thesis, two topics are studied: mathematical inequalities and non-linear quantum entanglement witnesses. First, various inequalities, like the Cauchy-Schwarz inequality (on finite dimensional vector spaces) and Jensen's inequality, along with their extensions and generalisations, are proved and discussed. The intimate relationship...