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arXiv · 1707.03934

On Local Unitary Equivalence of Two and Three-qubit States

Bao-zhi Sun·Shao-Ming Fei·Zhi-xi Wang
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Abstract

We study the local unitary equivalence for two and three-qubit mixed states by investigating the invariants under local unitary transformations. For two-qubit system, we prove that the determination of the local unitary equivalence of 2-qubits states only needs 14 or less invariants for arbitrary two-qubit states. Using the same method, we construct invariants for three-qubit mixed states. We prove that these invariants are sufficient to guarantee the LU equivalence of certain kind of three-qubit states. Also, we make a comparison with earlier works.

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Bao-zhi Sun, Shao-Ming Fei, Zhi-xi Wang. 2017-07-12. On Local Unitary Equivalence of Two and Three-qubit States. https://doi.org/10.1038/s41598-017-04717-2

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