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Special core tensors of multi-qubit states and the concurrency of three lines


Citation

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

Abstract

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.


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Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.1007/s11128-023-03939-w
Publisher: Springer
Keywords: Higher order singular value decomposition; Local unitary classification; Multi-qubit states; Quantum entanglement
Depositing User: Ms. Nur Faseha Mohd Kadim
Date Deposited: 02 Sep 2024 06:41
Last Modified: 02 Sep 2024 06:41
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1007/s11128-023-03939-w
URI: http://psasir.upm.edu.my/id/eprint/109127
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