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Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition

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Abstract

The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct several invariants of local unitary equivalence for general higher order tensors. Based on this new method, we study the coefficient tensors of 3-qubit states and obtain a necessary and sufficient criterion for local unitary equivalence of general tripartite states in terms of the CP decomposition. We also generalize this method to obtain some invariants of local unitary equivalence for general multi-partite qudits.

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Acknowledgments

The research is supported in part by Simons Foundation grant no. 523868 and National Natural Science Foundation of China grant nos. 12126351 and 12126314.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, China

    Jingmei Chang

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Naihuan Jing

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  1. Jingmei Chang
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  2. Naihuan Jing
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Correspondence to Jingmei Chang.

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Chang, J., Jing, N. Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition. Int J Theor Phys 61, 137 (2022). https://doi.org/10.1007/s10773-022-05106-w

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  • DOI: https://doi.org/10.1007/s10773-022-05106-w

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