Three Results in Quantum Physics

Abstract

This thesis is split into three disjoint sections. The first deals with two practical issues regarding the use of unitary 2-designs. A simplified description of how to generate elements of the smallest known unitary 2-design on qubits is given which should be usable even for people who do not have much experience with the mathematics of finite fields. The section also gives a new way to decompose an arbitrary element of the Clifford group into one and two qubit gates and is by far the simplest decomposition of its kind. The second section describes similarities and differences between a probabilistic formulation of classical mechanics and quantum mechanics, with the intention that it could become a resource for physics students to show that just because a physical phenomenon is strange it is not necessarily quantum. The third section is speculative and delves into the relationship between a highly theoretical field of quantum information science, Quantum Prover Interactive Proofs, and a highly practical area of quantum information science, error characterization. Previously unnoticed links are drawn between these fields with the intention that further research can provide fertile ground for both to flourish.