Higher-order singular value decomposition and the reduced density matrices of three qubits
In this paper, we demonstrate that higher order singular value decomposition (HOSVD) can be used to identify special states in three qubits by local unitary (LU) operations. Since the matrix unfoldings of three qubits are related to their reduced density matrices, HOSVD simultaneously diagonalizes t...
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2020
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my.upm.eprints.891872021-09-20T23:36:28Z http://psasir.upm.edu.my/id/eprint/89187/ Higher-order singular value decomposition and the reduced density matrices of three qubits Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini In this paper, we demonstrate that higher order singular value decomposition (HOSVD) can be used to identify special states in three qubits by local unitary (LU) operations. Since the matrix unfoldings of three qubits are related to their reduced density matrices, HOSVD simultaneously diagonalizes the one-body reduced density matrices of three qubits. From the all-orthogonality conditions of HOSVD, we computed the special states of three qubits. Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD. Springer 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/89187/1/VALUE.pdf Choong, Pak Shen and Zainuddin, Hishamuddin and Chan, Kar Tim and Said Husain, Sharifah Kartini (2020) Higher-order singular value decomposition and the reduced density matrices of three qubits. Quantum Information Processing, 19 (9). art. no. 338. pp. 1-21. ISSN 1570-0755; ESSN: 1573-1332 https://link.springer.com/article/10.1007/s11128-020-02848-6 10.1007/s11128-020-02848-6 |
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In this paper, we demonstrate that higher order singular value decomposition (HOSVD) can be used to identify special states in three qubits by local unitary (LU) operations. Since the matrix unfoldings of three qubits are related to their reduced density matrices, HOSVD simultaneously diagonalizes the one-body reduced density matrices of three qubits. From the all-orthogonality conditions of HOSVD, we computed the special states of three qubits. Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD. |
| format |
Article |
| author |
Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini |
| spellingShingle |
Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini Higher-order singular value decomposition and the reduced density matrices of three qubits |
| author_facet |
Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini |
| author_sort |
Choong, Pak Shen |
| title |
Higher-order singular value decomposition and the reduced density matrices of three qubits |
| title_short |
Higher-order singular value decomposition and the reduced density matrices of three qubits |
| title_full |
Higher-order singular value decomposition and the reduced density matrices of three qubits |
| title_fullStr |
Higher-order singular value decomposition and the reduced density matrices of three qubits |
| title_full_unstemmed |
Higher-order singular value decomposition and the reduced density matrices of three qubits |
| title_sort |
higher-order singular value decomposition and the reduced density matrices of three qubits |
| publisher |
Springer |
| publishDate |
2020 |
| url |
http://psasir.upm.edu.my/id/eprint/89187/1/VALUE.pdf http://psasir.upm.edu.my/id/eprint/89187/ https://link.springer.com/article/10.1007/s11128-020-02848-6 |
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1712286754608775168 |
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13.251813 |