Research

I’m interested in the mathematical structures that underlie quantum theory—especially how concepts from quantum information, integrable systems, and operator algebras come together to describe physical systems. Below are some of the main research projects I’ve worked on during my undergraduate studies.

Continuum Limits of Discrete Quantum Systems

Senior Thesis – UMass Dartmouth (2024–2025)

This project explores how the algebra of observables evolves when taking the continuum limit of discrete spin chains, with a focus on the Heisenberg XXX model. By applying the Bethe Ansatz and tools from operator algebra, I study the emergence of von Neumann factors like Type I_∞ and Type III in the infinite-degree-of-freedom limit. The work connects ideas from quantum integrability, locality, and quantum field theory.

Single-Photon Blockade with Weak Nonlinearities

REU – Institute for Nuclear Theory, University of Washington (Summer 2024)

I helped simulate single-photon blockade using a weak Kerr-type nonlinearity in a theoretical quantum optics setup. We used QuTiP to solve the Lindblad equation and computed correlation functions to verify Fock state generation. This project deepened my understanding of open quantum systems and photon statistics.

Quantum Information Measures via Conditional Probabilities

Independent Project – UMass Dartmouth (2023)

I investigated alternative ways to define quantum information measures using conditional probabilities. The goal was to create more intuitive tools for characterizing quantum entanglement and non-classical behavior. This early project helped develop my interest in quantum foundations and information theory.

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';