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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Bibliographic Details
Published inQuantum information processing Vol. 19; no. 9
Main Authors Choong, Pak Shen, Zainuddin, Hishamuddin, Chan, Kar Tim, Husain, Sh. K. Said
Format Journal Article
LanguageEnglish
Published New York Springer US 2020
Springer Nature B.V
Subjects
Data Structures and Information Theory
Density
Mathematical Physics
Orthogonality
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Singular value decomposition
Spintronics
Local unitary equivalence
Quantum entanglement
Three qubits
15A69
Higher-order singular value decomposition
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-020-02848-6