PhD Proposal: Cameron Hahn

ADVISOR: Dr. Fabio Anza

TITLE: A GEOMETRIC THEORY OF QUANTUM ENSEMBLES: INFORMATION, DYNAMICS, AND BENCHMARKING

ABSTRACT: Behind every density matrix there is an ensemble of pure states, and infinitely many ensembles produce the same matrix. Which ensemble a system realizes is fixed by how the system was prepared or measured, and that information is discarded when we pass to the density matrix. In this thesis I will treat ensembles of pure states directly as a fundamental notion of quantum state, using Geometric Quantum Mechanics to describe them as probability measures on the manifold of pure states and build new theoretical tools to study and understand their properties. These tools will fall into three areas. The first is information theoretic, where the quantities we use to characterize the resource content of states must be reformulated for ensembles. The second is dynamical, where the evolution of an ensemble becomes a problem of probability transport across the manifold of pure states. The third is benchmarking, where a device's ability to produce a desired ensemble, rather than just a desired density matrix, must be better understood. Since experiments can now access ensembles directly, a theory written only for the density matrix leaves information in the ensemble unaccounted for. Treating the ensemble directly as the quantum state allows this information to be made precise, broadening our understanding of how extra information about measurement outcomes or preparation protocols plays a role in quantum information theory.