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...