On Local Unitary Equivalence of Two and Three-qubit States

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 tw...

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Autores principales: Sun, Bao-Zhi, Fei, Shao-Ming, Wang, Zhi-Xi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5501876/
https://www.ncbi.nlm.nih.gov/pubmed/28687739
http://dx.doi.org/10.1038/s41598-017-04717-2
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author Sun, Bao-Zhi
Fei, Shao-Ming
Wang, Zhi-Xi
author_facet Sun, Bao-Zhi
Fei, Shao-Ming
Wang, Zhi-Xi
author_sort Sun, Bao-Zhi
collection PubMed
description 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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spelling pubmed-55018762017-07-10 On Local Unitary Equivalence of Two and Three-qubit States Sun, Bao-Zhi Fei, Shao-Ming Wang, Zhi-Xi Sci Rep Article 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. Nature Publishing Group UK 2017-07-07 /pmc/articles/PMC5501876/ /pubmed/28687739 http://dx.doi.org/10.1038/s41598-017-04717-2 Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Sun, Bao-Zhi
Fei, Shao-Ming
Wang, Zhi-Xi
On Local Unitary Equivalence of Two and Three-qubit States
title 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_short On Local Unitary Equivalence of Two and Three-qubit States
title_sort on local unitary equivalence of two and three-qubit states
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5501876/
https://www.ncbi.nlm.nih.gov/pubmed/28687739
http://dx.doi.org/10.1038/s41598-017-04717-2
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