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

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Pak Shen Choong , Hishamuddin Zainuddin , Kar Tim Chan , Sharifah Kartini Said Husain ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2301.05953

Classification of multipartite states aims to obtain a set of operationally useful and finite entanglement classes under the action of either local unitary (LU) or stochastic local operation and classical communication (SLOCC). In this work, we propose a computationally simple approach to find these classes by using higher order singular value decomposition (HOSVD) and the concurrency of three lines. Since HOSVD simultaneously diagonalizes the one-body reduced density matrices (RDM) of multipartite states, the core tensor of multipartite states is the pure-state representation of such simultaneously diagonalized one-body RDM. We identified the special core tensors of three and four qubits, which are also genuinely entangled by default. The special core tensors are further categorized into families of states based on their first $n$-mode singular values, $σ_1^{(i)2}$. The current proposal is limited to multi-qubit system, but it scales well with large multi-qubit systems and produces a finite number of families of states.

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Qubit Multipartite Unitary state Mathematics Tensor (intrinsic definition) Concatenation (mathematics) Multipartite entanglement Quantum entanglement Pure mathematics Quantum Quantum mechanics Combinatorics Physics Squashed entanglement Law Political science

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2301.05953
PDF: https://arxiv.org/pdf/2301.05953
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DOI: https://doi.org/10.48550/arxiv.2301.05953

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

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Publication year: 2023

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Publication date: 2023-01-14

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Authors: Pak Shen Choong, Hishamuddin Zainuddin, Kar Tim Chan, Sharifah Kartini Said Husain

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Concepts: Qubit, Multipartite, Unitary state, Mathematics, Tensor (intrinsic definition), Concatenation (mathematics), Multipartite entanglement, Quantum entanglement, Pure mathematics, Quantum, Quantum mechanics, Combinatorics, Physics, Squashed entanglement, Law, Political science

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