The Language of the Quantum: A Philosophical and Formal Study of Quantum Foundations

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering

Final Year Thesis Oral Defense

Title: "The Language of the Quantum: A Philosophical and Formal Study of 
Quantum Foundations"

by

MOK Ching Hei

Abstract:

Quantum theory is one of the most successful theories in the history of 
science. Despite its unparalleled empirical success and technological 
impact, it defies classical intuition with phenomena like superposition, 
entanglement and the resulting non-locality, challenging traditional 
assumptions about the nature of the universe. This thesis explores quantum 
foundations through the lenses of philosophy, logic, and mathematics, aiming 
to understand the connection between the formal mathematical framework of 
quantum mechanics and its philosophical and metaphysical interpretations.

We begin with a formal reconstruction of quantum mechanics, establishing its 
axioms, mathematical structure, and information-theoretic implications, 
including a detailed treatment of the measurement problem. The thesis then 
addresses three core conceptual challenges in constructing a satisfactory 
theory of quantum mechanics – reality, locality and contextuality – through 
formal definitions and analysis of key theorems.

Beyond literature review, we explore a generalisation of quantum information 
theory and provide a proof of the Choi-Jamiolkowski Isomorphism within this 
model. We also explore a new interpretation of quantum mechanics and 
formulate the PBR |0⟩ |+⟩ scenario within this framework. Throughout, a 
unified notational system and strong emphasis on mathematical rigor and 
philosophical clarity guide the development of ideas.


Date            : 2 May 2025 (Friday)

Time            : 13:00 - 13:40

Venue           : Room 5566 (near lifts 27/28), HKUST

Advisor         : Prof. DING Cunsheng

2nd Reader      : Dr. SONG Yangqiu