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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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/52358/ http://psasir.upm.edu.my/id/eprint/52358/1/6.%20Choong.pdf |
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| author | Choong, Pak Shen Zainuddin, Hishamuddin Rakhimov, Isamiddin Sattarovich |
| author_facet | Choong, Pak Shen Zainuddin, Hishamuddin Rakhimov, Isamiddin Sattarovich |
| author_sort | Choong, Pak Shen |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T10:32:26Z |
| format | Article |
| id | upm-52358 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:32:26Z |
| publishDate | 2016 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | Choong, Pak Shen Zainuddin, Hishamuddin Rakhimov, Isamiddin Sattarovich Multilinear singular value decomposition for two qubits |
| title | 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_short | Multilinear singular value decomposition for two qubits |
| title_sort | multilinear singular value decomposition for two qubits |
| 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 |