Master Thesis Defense: Hans Michael Christensen

The Many Faces of Geometric Phases: Underdetermination of Geometric Phases in Quantum Theory

In recent years, several researchers have suggested that implementations of phase gates, that purely rely on geometric phases, are more robust than other protocols. We argue that this intuition presupposes that the geometric phase contribution is uniquely defined. Therefore, we set out to investigate whether the geometric phase contribution is uniquely defined given a physical protocol. We find that there exist empirically equivalent descriptions which assign the geometric phase contribution different values. Namely different choices of interaction picture. This casts serious doubt on the intuition that purely geometric protocols are more robust than other protocols since the geometric nature of the protocol is only true for certain interaction pictures. We introduce a new interaction picture independent definition of the geometric phase. This allows us to arrive at several novel geometric results. In the end, we find that the new geometric phase presupposes other conventions, and is therefore also not uniquely defined. We hope that our considerations will inspire researchers, who argue for the robustness of geometric protocols, to scrutinize their choice of convention, and thereby gain insights into the mechanisms that lead to robust protocols.