UPM Institutional Repository

Multilinear singular value decomposition for two qubits


Choong, Pak Shen and Zainuddin, Hishamuddin and Rakhimov, Isamiddin Sattarovich (2016) Multilinear singular value decomposition for two qubits. Malaysian Journal of Mathematical Sciences, 10 (spec. Aug.). pp. 69-83. ISSN 1823-8343; ESSN: 2289-750X


Schmidt decomposition has been used in the local unitary (LU) classification of bipartite quantum states for some time. In order to generalize the LU classification of bipartite quantum states into multipartite quantum states, higher order singular value decomposition (HOSVD) is introduced but specific examples have not been explicitly worked out. In this pedagogical paper, we would like to work out such details in two qubits since the LU classification of two qubits is well known. We first demonstrate the method of HOSVD in two-qubit systems and discuss its properties. In terms of the LU classification of two-qubit states, some subtle differences in the stabilizer groups of entanglement classes are noticed when Schmidt decomposition is substituted by HOSVD. To reconcile the differences between the two, further studies are needed.

Download File

6. Choong.pdf

Download (480kB) | Preview

Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
Publisher: Institute for Mathematical Research, Universiti Putra Malaysia
Notes: Special issue: The 7th International Conference on Research and Education in Mathematics (ICREM7)
Keywords: Higher order singular value decomposition; Two qubits; Local unitary operation
Depositing User: Nabilah Mustapa
Date Deposited: 05 Jun 2017 09:34
Last Modified: 05 Jun 2017 09:34
URI: http://psasir.upm.edu.my/id/eprint/52358
Statistic Details: View Download Statistic

Actions (login required)

View Item View Item