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A GEOMETRY OF ENTANGLEMENT

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Date Issued:
2022
Abstract/Description:
We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher’s singlet state triangle inequality, which used an entropic-based distance to capture the strange properties of entanglement using geometric-based inequalities. Schumacher uses classical entropy and can only describe the geometry of bipartite states. We extend his approach by using von Neumann entropy to create an entanglement monotone that can be generalized for higher dimensional systems. We achieve this by utilizing recent definitions for entropic areas, volumes, and higher dimensional volumes for multipartite which we introduce in this thesis. This enables us to differentiate systems with high quantum correlation from systems with low quantum correlation and differentiate between different types of multi-partite entanglement. It also enable us to describe some of the strange properties of quantum entanglement using simple geometrical inequalities. Our geometrization of entanglement provides new insight into quantum entanglement. Perhaps by constructing well motivated geometrical structures (e.g. relations among areas, volumes ...), a set of trivial geometrical inequalities can reveal some of the complex properties of higher-dimensional entanglement in multi-partite systems. We provide numerous illustrative applications of this approach.
Title: A GEOMETRY OF ENTANGLEMENT.
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Name(s): Mostafanazhad, Shahabeddin Aslmarand , author
Wille, Luc T. Wille, Thesis advisor
Florida Atlantic University, Degree grantor
Department of Physics
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2022
Date Issued: 2022
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 79 p.
Language(s): English
Abstract/Description: We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher’s singlet state triangle inequality, which used an entropic-based distance to capture the strange properties of entanglement using geometric-based inequalities. Schumacher uses classical entropy and can only describe the geometry of bipartite states. We extend his approach by using von Neumann entropy to create an entanglement monotone that can be generalized for higher dimensional systems. We achieve this by utilizing recent definitions for entropic areas, volumes, and higher dimensional volumes for multipartite which we introduce in this thesis. This enables us to differentiate systems with high quantum correlation from systems with low quantum correlation and differentiate between different types of multi-partite entanglement. It also enable us to describe some of the strange properties of quantum entanglement using simple geometrical inequalities. Our geometrization of entanglement provides new insight into quantum entanglement. Perhaps by constructing well motivated geometrical structures (e.g. relations among areas, volumes ...), a set of trivial geometrical inequalities can reveal some of the complex properties of higher-dimensional entanglement in multi-partite systems. We provide numerous illustrative applications of this approach.
Identifier: FA00013912 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2022.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Quantum systems
Geometry
Quantum entanglement
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013912
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.