Linear inequalities related to quantum entanglement theory

Abstract

In this thesis, we will consider various linear inequalities relating the entries and eigenvalues of certain types of matrices. Our approach will consist of constructing inequalities which set bounds on the eigenvalues of entanglement witnesses, a type of matrix of interest to quantum information theory. We will then consider what these can tell us about the relation between the off-diagonal entries and eigenvalues of positive semidefinite matrices.