Date of Award

Fall 2024

Language

English

Embargo Period

11-13-2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Physics

Program

Physics

First Advisor

Philip Goyal

Committee Members

Herbert Fotso, Philip Goyal, Jonathan Petruccelli, Daniel Robbins, Rongwei Yang

Keywords

Foundation of Quantum Theory, Reconstruction of Quantum Theory, Quantum Information, Information Theory, Bayesian Analysis

Subject Categories

Quantum Physics

Abstract

This thesis examines the concept of information within the realm of quantum physics, investigating the nuanced relationship between information and physical laws as applied to quantum systems. With no consensus on a single definition of information in the physical sciences, our exploration is partitioned into two significant studies, each addressing distinct aspects of information in quantum contexts.

In the first study, we concentrate on the information that can be obtained from measurement results on identical quantum systems. The traditional approach of using Shannon entropy is limited due to its applicability primarily to discrete probability distributions. By incorporating a Bayesian update framework, we redefine the process of information gain, which allows for a more nuanced understanding of information dynamics within quantum measurements. Key findings from this approach include a novel expression for quantifying information gain and a principle for the selection of appropriate priors, specifically employing Jeffreys’ prior for binomial distributions. The study also highlights the effectiveness of Jeffreys' binomial prior in optimizing quantum communication scenarios, such as maximizing the information deciphered by a receiver (Bob) from a sender’s (Alice) message-encoded qubits.

The second study shifts focus to the foundational aspects of quantum theory itself, employing an informational approach to reconstruct the theory’s underlying structure. Here, quantum measurements are conceptualized as finite outcome questions linked through classical logical operations within systems extending beyond binary dimensions. By introducing intuitive informational postulates, we achieve a partial reconstruction of quantum theory, particularly within systems characterized by prime number dimensions. This reconstruction yields rich connections between classical logical gates, generalized Pauli matrices, and mutually unbiased bases, enhancing our comprehension of how information flows during measurements on maximally entangled systems.

License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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