Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines

This research studied the classification problem of multipartite states. Since the Hilbert space of a multipartite system has a tensor product structure, we made use of a tensor decomposition, called higher order singular value decomposition (HOSVD) to solve the problem. We focused on finding the...

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Main Author:	Choong, Pak Shen
Format:	Thesis
Language:	English
Published:	2022
Subjects:	Quantum computing Mathematical physics
Online Access:	http://psasir.upm.edu.my/id/eprint/113995/1/113995.pdf
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spelling	my-upm-ir.1139952024-11-29T01:29:48Z Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines 2022-12 Choong, Pak Shen This research studied the classification problem of multipartite states. Since the Hilbert space of a multipartite system has a tensor product structure, we made use of a tensor decomposition, called higher order singular value decomposition (HOSVD) to solve the problem. We focused on finding the solutions to the set of allorthogonality conditions from HOSVD to obtain a complete classification of three qubits. Based on the relationship between the set of first n-mode singular values, σ(n)2 1 , we identified three possible cases that contain all the entanglement classes of three qubits. An entanglement polytope was illustrated to demonstrate how the entanglement classes of three qubits change with respect to σ(n)2 1 , which is in accordance with the existing literature. The geometrical significance of our classification method was studied by finding the stabilizer dimensions of all the entanglement classes of three qubits. We found that different entanglement classes of three qubits have different stabilizer dimensions. Furthermore, by making use of the concurrency of three lines, we generalized our classification approach for multi-qubit states, which is computationally simple and yet capable of producing a finite number of family of states. As a demonstration, we classified four-qubit states with our proposal and found four possible cases that contain the genuinely entangled four-qubit states. Quantum computing Mathematical physics 2022-12 Thesis http://psasir.upm.edu.my/id/eprint/113995/ http://psasir.upm.edu.my/id/eprint/113995/1/113995.pdf text en public http://ethesis.upm.edu.my/id/eprint/18052 doctoral Universiti Putra Malaysia Quantum computing Mathematical physics Zainuddin, Hishamuddin
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Zainuddin, Hishamuddin
topic	Quantum computing Mathematical physics
spellingShingle	Quantum computing Mathematical physics Choong, Pak Shen Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
description	This research studied the classification problem of multipartite states. Since the Hilbert space of a multipartite system has a tensor product structure, we made use of a tensor decomposition, called higher order singular value decomposition (HOSVD) to solve the problem. We focused on finding the solutions to the set of allorthogonality conditions from HOSVD to obtain a complete classification of three qubits. Based on the relationship between the set of first n-mode singular values, σ(n)2 1 , we identified three possible cases that contain all the entanglement classes of three qubits. An entanglement polytope was illustrated to demonstrate how the entanglement classes of three qubits change with respect to σ(n)2 1 , which is in accordance with the existing literature. The geometrical significance of our classification method was studied by finding the stabilizer dimensions of all the entanglement classes of three qubits. We found that different entanglement classes of three qubits have different stabilizer dimensions. Furthermore, by making use of the concurrency of three lines, we generalized our classification approach for multi-qubit states, which is computationally simple and yet capable of producing a finite number of family of states. As a demonstration, we classified four-qubit states with our proposal and found four possible cases that contain the genuinely entangled four-qubit states.
format	Thesis
qualification_level	Doctorate
author	Choong, Pak Shen
author_facet	Choong, Pak Shen
author_sort	Choong, Pak Shen
title	Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
title_short	Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
title_full	Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
title_fullStr	Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
title_full_unstemmed	Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
title_sort	classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines
granting_institution	Universiti Putra Malaysia
publishDate	2022
url	http://psasir.upm.edu.my/id/eprint/113995/1/113995.pdf
_version_	1818586178484436992

Classification of multi-qubit states with higher order singular value decompositon and concurrency of three lines

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