Multilinear singular value decomposition for two qubits

Multilinear singular value decomposition for two qubits

Schmidt decomposition has been used in the local unitary (LU) classification of bipartite quantum states for some time. In order to generalize the LU classification of bipartite quantum states into multipartite quantum states, higher order singular value decomposition (HOSVD) is introduced but speci...

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Main Authors: Choong, Pak Shen, Zainuddin, Hishamuddin, Rakhimov, Isamiddin Sattarovich
Format: Article
Language:English
Published: Institute for Mathematical Research, Universiti Putra Malaysia 2016
Online Access:http://psasir.upm.edu.my/id/eprint/52358/
http://psasir.upm.edu.my/id/eprint/52358/
http://psasir.upm.edu.my/id/eprint/52358/1/6.%20Choong.pdf
id upm-52358
recordtype eprints
spelling upm-523582017-06-05T09:34:33Z http://psasir.upm.edu.my/id/eprint/52358/ Multilinear singular value decomposition for two qubits Choong, Pak Shen Zainuddin, Hishamuddin Rakhimov, Isamiddin Sattarovich Schmidt decomposition has been used in the local unitary (LU) classification of bipartite quantum states for some time. In order to generalize the LU classification of bipartite quantum states into multipartite quantum states, higher order singular value decomposition (HOSVD) is introduced but specific examples have not been explicitly worked out. In this pedagogical paper, we would like to work out such details in two qubits since the LU classification of two qubits is well known. We first demonstrate the method of HOSVD in two-qubit systems and discuss its properties. In terms of the LU classification of two-qubit states, some subtle differences in the stabilizer groups of entanglement classes are noticed when Schmidt decomposition is substituted by HOSVD. To reconcile the differences between the two, further studies are needed. Institute for Mathematical Research, Universiti Putra Malaysia 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/52358/1/6.%20Choong.pdf Choong, Pak Shen and Zainuddin, Hishamuddin and Rakhimov, Isamiddin Sattarovich (2016) Multilinear singular value decomposition for two qubits. Malaysian Journal of Mathematical Sciences, 10 (spec. Aug.). pp. 69-83. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol10saugust/6.%20Choong.pdf
repository_type Digital Repository
institution_category Local University
institution Universiti Putra Malaysia
building UPM Institutional Repository
collection Online Access
language English
description Schmidt decomposition has been used in the local unitary (LU) classification of bipartite quantum states for some time. In order to generalize the LU classification of bipartite quantum states into multipartite quantum states, higher order singular value decomposition (HOSVD) is introduced but specific examples have not been explicitly worked out. In this pedagogical paper, we would like to work out such details in two qubits since the LU classification of two qubits is well known. We first demonstrate the method of HOSVD in two-qubit systems and discuss its properties. In terms of the LU classification of two-qubit states, some subtle differences in the stabilizer groups of entanglement classes are noticed when Schmidt decomposition is substituted by HOSVD. To reconcile the differences between the two, further studies are needed.
format Article
author Choong, Pak Shen
Zainuddin, Hishamuddin
Rakhimov, Isamiddin Sattarovich
spellingShingle Choong, Pak Shen
Zainuddin, Hishamuddin
Rakhimov, Isamiddin Sattarovich
Multilinear singular value decomposition for two qubits
author_facet Choong, Pak Shen
Zainuddin, Hishamuddin
Rakhimov, Isamiddin Sattarovich
author_sort Choong, Pak Shen
title Multilinear singular value decomposition for two qubits
title_short Multilinear singular value decomposition for two qubits
title_full Multilinear singular value decomposition for two qubits
title_fullStr Multilinear singular value decomposition for two qubits
title_full_unstemmed Multilinear singular value decomposition for two qubits
title_sort multilinear singular value decomposition for two qubits
publisher Institute for Mathematical Research, Universiti Putra Malaysia
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/52358/
http://psasir.upm.edu.my/id/eprint/52358/
http://psasir.upm.edu.my/id/eprint/52358/1/6.%20Choong.pdf
first_indexed 2018-09-07T18:16:58Z
last_indexed 2018-09-07T18:16:58Z
_version_ 1610973675712937984

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