Graduation Year
2024
Date of Submission
12-2024
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Physics
Reader 1
Dr. Kevin Setter
Reader 2
Dr. Adam Landsberg
Terms of Use & License Information
Rights Information
© 2023 Brian Lee
Abstract
In the decoherence account of quantum mechanics, a choice of particular tensor product structure (a particular partition of system into subsystems) is assumed. We explore whether it is possible to relax this arbitrary choice by requiring that a valid tensor product structure admits a quasi-classical description. Such tensor product structures are said to be quasi-classical or decoherence-selected tensor product structures. This project generalizes a 2-qubit quasi-classical tensor product structure selection algorithm to an n-qubit selection algorithm, which allows us to, for the first time, consider the relationship between decoherence-selected tensor product structures and locality-selected tensor product structures. To generalize the algorithm, we make novel use of a local unitary equivalence check algorithm from [ 1]. For n-qubit systems in the infinite temperature limit, we find that there always exists an exact quasi-classical tensor product structure. We prove a theorem that characterizes all quasi-classical tensor product structures for any n-qubit system in the infinite temperature limit. We find that quasi-classical tensor product structures are precisely the tensor product structures generated by either non-interacting or diagonal Hamiltonians. We also find formulae for the mean and standard deviation of entanglement entropy growth within local unitary orbits of a tensor product structure, quantitatively showing that some tensor product structures are better than others.
Recommended Citation
Lee, Brian, "Existence of Well-Defined Pointer Observable Selects Tensor Product Factorizations of Quantum Systems" (2024). CMC Senior Theses. 3479.
https://scholarship.claremont.edu/cmc_theses/3479
