On Local Unitary Equivalence of Two and Three-qubit States

Bao-Zhi Sun, Shao-Ming Fei, and Zhi-Xi Wang

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Submission date: 28. Aug. 2017
Pages: 14
published in: Scientific Reports, 7 (2017), art-no. 4869 
DOI number (of the published article): 10.1038/s41598-017-04717-2
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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.