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This thesis proposes a novel measure of quantum entanglement that can be used to characterize the degree of entanglement of three (or more) parties. Entanglement has been studied and used in many ways since Erwin Schrödinger defined and named it in 1935, but quantifiable measures of the degree of entanglement, known as concurrence, have long been limited to two quantum parties (two qubits, for example). Three-qubit states, which are known to be more reliable for teleportation of qubits than two-party entanglement, run into difficult criteria in entanglement-measure theory, and efforts to quantify a measure of genuine multipartite entanglement (GME) for three-qubit states have frustrated quantum theorists for decades. This work explores a novel triangle inequality among three-qubit concurrences and demonstrates that the area of a 3-qubit concurrence triangle provides the first measure of GME for 3-qubit systems. The proposed measure, denoted “entropic fill,” has an intuitive interpretation related to the hypervolume of a simplex describing the relation between any subpart of the system with the rest. Importantly, entropic fill not only gives the first successful measure of GME for 3-party quantum systems, but also can be generalized into higher dimensions, providing a path to quantify quantum entanglement among many parties.
List of contents
Preliminary: Hilbert Space and Linear Operators.- Review: Bipartite Entanglement.- Breakthrough: Multipartite Entanglement.- Geometric Journey: Multipartite Entanglement.- Concluding Remarks.
About the author
Songbo Xie started his academic journey at Shanghai Jiao Tong University in 2013 and obtained his Bachelor of Science degree in Physics in 2017. That same year, he was admitted to the University of Rochester for doctoral studies, receiving his Master of Arts degree in Physics in 2019 and his Doctor of Philosophy degree in Physics in 2024.
Throughout his doctoral studies, Songbo Xie focused his research on quantum physics, guided by Professor Joseph H.~Eberly. His research interests include quantum information, quantum computing, quantum many-body systems, quantum simulation, quantum thermodynamics, and the foundations of quantum mechanics.
One of his academic achievements during his doctoral studies was the development of an innovative geometric method to quantify ``genuine multipartite entanglement,'' a distinct form of entanglement that extends beyond two-party systems. He employed the hypervolume of geometric simplices in his approach, allowing for a deeper understanding and exploration of the complex physical properties exhibited within quantum many-body systems.
Summary
This thesis proposes a novel measure of quantum entanglement that can be used to characterize the degree of entanglement of three (or more) parties. Entanglement has been studied and used in many ways since Erwin Schrödinger defined and named it in 1935, but quantifiable measures of the degree of entanglement, known as concurrence, have long been limited to two quantum parties (two qubits, for example). Three-qubit states, which are known to be more reliable for teleportation of qubits than two-party entanglement, run into difficult criteria in entanglement-measure theory, and efforts to quantify a measure of genuine multipartite entanglement (GME) for three-qubit states have frustrated quantum theorists for decades. This work explores a novel triangle inequality among three-qubit concurrences and demonstrates that the area of a 3-qubit concurrence triangle provides the first measure of GME for 3-qubit systems. The proposed measure, denoted “entropic fill,” has an intuitive interpretation related to the hypervolume of a simplex describing the relation between any subpart of the system with the rest. Importantly, entropic fill not only gives the first successful measure of GME for 3-party quantum systems, but also can be generalized into higher dimensions, providing a path to quantify quantum entanglement among many parties.
