On Local Unitary Equivalence of Two and Three-qubit States
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 arb...
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Nature Publishing Group
2017-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-017-04717-2 |
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doaj-ce4e10564b3c44cdaf9853e3f94f4c6f2020-12-08T02:36:34ZengNature Publishing GroupScientific Reports2045-23222017-07-01711610.1038/s41598-017-04717-2On Local Unitary Equivalence of Two and Three-qubit StatesBao-Zhi Sun0Shao-Ming Fei1Zhi-Xi Wang2School of Mathematics, Qufu Normal UniversitySchool of Mathematical Sciences, Capital Normal UniversitySchool of Mathematical Sciences, Capital Normal UniversityAbstract 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.https://doi.org/10.1038/s41598-017-04717-2 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bao-Zhi Sun Shao-Ming Fei Zhi-Xi Wang |
| spellingShingle |
Bao-Zhi Sun Shao-Ming Fei Zhi-Xi Wang On Local Unitary Equivalence of Two and Three-qubit States Scientific Reports |
| author_facet |
Bao-Zhi Sun Shao-Ming Fei Zhi-Xi Wang |
| author_sort |
Bao-Zhi Sun |
| title |
On Local Unitary Equivalence of Two and Three-qubit States |
| title_short |
On Local Unitary Equivalence of Two and Three-qubit States |
| title_full |
On Local Unitary Equivalence of Two and Three-qubit States |
| title_fullStr |
On Local Unitary Equivalence of Two and Three-qubit States |
| title_full_unstemmed |
On Local Unitary Equivalence of Two and Three-qubit States |
| title_sort |
on local unitary equivalence of two and three-qubit states |
| publisher |
Nature Publishing Group |
| series |
Scientific Reports |
| issn |
2045-2322 |
| publishDate |
2017-07-01 |
| description |
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. |
| url |
https://doi.org/10.1038/s41598-017-04717-2 |
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