Graduation Year

2023

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Physics

Reader 1

Kevin Setter

Reader 2

Adam Landsberg

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© 2022 Marissa M Singh

Abstract

In recent decades, the program of Decoherence has helped clarify how features of the classical world emerge from Quantum Mechanics. According to Decoherence, the interaction between a system and its environment dynamically selects certain system states — the pointer states — that exhibit predictable, classical behavior while their superpositions rapidly decohere. However, most Decoherence studies to date pre-suppose a preferred division of the world into “system” and “environment”, corresponding to a preferred choice of Tensor Product Structure (TPS) on the Hilbert Space of states. A few previous works have suggested that the existence of a well-defined pointer observable may be used to dynamically select one TPS over another (given only the barebones data of a Hilbert Space of states and Hamiltonian operator). In this thesis, we adapt the “in-principle” algorithm of \citep{CARROLL} to a system of multiple qubits. We streamline the algorithm, incorporate the extra principle Democracy of Qubits, and code it using NumPy. Using gradient descent, the code is able to perform a search to identify an optimal TPS. Separately, the local unitary invariants of \citep{SUN} are used to check whether or not the outputs of gradient descent belong to the same local unitary orbits and therefore the same TPS. We find that some TPSes are better than others for the 2-qubit system, but there does not appear to be a unique minimum TPS.

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