Date of Award

Spring 2026

Language

English

Embargo Period

5-10-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Physics

Program

Physics

First Advisor

Philip Goyal

Committee Members

Philip Goyal, Jesse Ernst, Daniel Robbins, Jonathan Petruccelli, Rongwei Yang

Keywords

Quantum Measurements, Quantum State Tomography, Information Theory, POVM Measurements

Subject Categories

Quantum Physics

Abstract

This thesis will focus on deriving informationally-optimal quantum state tomographic measurements on single-qubit systems, with the definition of informationally optimal to be defined as those measurements which maximize the average information gain. The informationally-optimal measurements that will be covered include projective measurements (formally building off of the work of [1] and putting it on firm, information-theoretic foundations), and more general types of quantum measurements called directional (also known as rank-one) positive operator-valued measure (POVM) measurements, and, finally, adaptive directional POVM measurements.

For projective measurements, we build on the work of Wootters and Fields ([1]) and show, via analytical methods and maximizing the average information gained from the measurements, that orthogonal projective measurements are optimal.

We then go on to define what we call directional POVMs, which are POVMs whose elements are given by weighted projection operators. We consider these measurements in the context of static quantum state tomography (QST), wherein we use the same choice of measurement throughout our analysis/experiment. By examining these directional POVMs acting on single qubit systems, we show that the most informationally optimal of these types of measurements are informationally complete directional POVMs that are both minimal, informationally complete (MIC) and symmetric, informationally complete (SIC) POVMs, simultaneously.

Finally, we deal with the case of adaptive directional POVM measurements.

License

This work is licensed under the University at Albany Standard Author Agreement.

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