Special core tensors of multi-qubit states and the concurrency of three lines
In this work, we propose a computationally simple approach to identify the local unitary (LU) entanglement classes of multi-qubit states by higher-order singular value decomposition (HOSVD). For multipartite states, HOSVD simultaneously diagonalizes their one-body reduced density matrices (RDM) by L...
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| Format: | Article |
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Springer
2023
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| _version_ | 1811137882148044800 |
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| author | Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini |
| author_facet | Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini |
| author_sort | Choong, Pak Shen |
| collection | UPM |
| description | In this work, we propose a computationally simple approach to identify the local unitary (LU) entanglement classes of multi-qubit states by higher-order singular value decomposition (HOSVD). For multipartite states, HOSVD simultaneously diagonalizes their one-body reduced density matrices (RDM) by LU actions. Therefore, the zeros of the all-orthogonality conditions due to HOSVD, also known as the core tensors, are the pure-state representations of such simultaneously diagonalized one-body RDM for a given multipartite state. By using the concurrency of three lines, we simplified the calculations and coarse-grained the classification into a finite number of families of states based on the square of their first n-mode singular values, σ1(n)2 . These special core tensors are genuinely entangled by default. For three and four qubits, we identified two and four families of states respectively. A generalization of the algorithm to multi-qubit states is provided. |
| first_indexed | 2024-09-25T03:41:21Z |
| format | Article |
| id | upm.eprints-109127 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-09-25T03:41:21Z |
| publishDate | 2023 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-1091272024-09-02T06:41:22Z http://psasir.upm.edu.my/id/eprint/109127/ Special core tensors of multi-qubit states and the concurrency of three lines Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini In this work, we propose a computationally simple approach to identify the local unitary (LU) entanglement classes of multi-qubit states by higher-order singular value decomposition (HOSVD). For multipartite states, HOSVD simultaneously diagonalizes their one-body reduced density matrices (RDM) by LU actions. Therefore, the zeros of the all-orthogonality conditions due to HOSVD, also known as the core tensors, are the pure-state representations of such simultaneously diagonalized one-body RDM for a given multipartite state. By using the concurrency of three lines, we simplified the calculations and coarse-grained the classification into a finite number of families of states based on the square of their first n-mode singular values, σ1(n)2 . These special core tensors are genuinely entangled by default. For three and four qubits, we identified two and four families of states respectively. A generalization of the algorithm to multi-qubit states is provided. Springer 2023-05 Article PeerReviewed Choong, Pak Shen and Zainuddin, Hishamuddin and Chan, Kar Tim and Said Husain, Sharifah Kartini (2023) Special core tensors of multi-qubit states and the concurrency of three lines. Quantum Information Processing, 22 (5). art. no. 193. pp. 1-30. ISSN 1570-0755; ESSN: 1573-1332 https://link.springer.com/article/10.1007/s11128-023-03939-w?error=cookies_not_supported&code=474cfc27-c36f-4a6b-a9ae-030a092a1441 10.1007/s11128-023-03939-w |
| spellingShingle | Choong, Pak Shen Zainuddin, Hishamuddin Chan, Kar Tim Said Husain, Sharifah Kartini Special core tensors of multi-qubit states and the concurrency of three lines |
| title | Special core tensors of multi-qubit states and the concurrency of three lines |
| title_full | Special core tensors of multi-qubit states and the concurrency of three lines |
| title_fullStr | Special core tensors of multi-qubit states and the concurrency of three lines |
| title_full_unstemmed | Special core tensors of multi-qubit states and the concurrency of three lines |
| title_short | Special core tensors of multi-qubit states and the concurrency of three lines |
| title_sort | special core tensors of multi qubit states and the concurrency of three lines |
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