Limiting behaviours in physics: From Duality to Super-resolution

Abstract

In this thesis, we discuss several phenomena exhibiting `limiting behaviour' in physics. This includes the duality principle, delegated quantum computation, and super-resolution. The duality principle places a limit on the coexistence of wave and particle behaviours. We develop a framework that explains apparent violations of this principle while staying within the scope of quantum mechanics. In addition, we relate the duality principle to the sub-fidelity and weak-values. We also show that the maximum recoverable coherence of a qubit has a sharp transition from 0 to 1 when we have access to half of the environment to which the qubit is correlated. Delegated quantum computation consists of a computational weak client who wishes to delegate a complex quantum computation to a powerful quantum server. We develop a new protocol for delegated quantum computation requiring less quantum power than its predecessor. Finally, we develop and test a new theory for eigenmode super-resolution.