Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices

Since two quantum states that are local unitary (LU) equivalent have the same amount of entanglement, it is meaningful to find a practical method to determine the LU equivalence of given quantum states. In this paper, we present a valid process to find the unitary tensor product decomposition for an...

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Autores principales: Wang, Jing, Liu, Xiaoqi, Xu, Li, Li, Ming, Li, Lei, Shen, Shuqian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10452990/
https://www.ncbi.nlm.nih.gov/pubmed/37628169
http://dx.doi.org/10.3390/e25081139
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author Wang, Jing
Liu, Xiaoqi
Xu, Li
Li, Ming
Li, Lei
Shen, Shuqian
author_facet Wang, Jing
Liu, Xiaoqi
Xu, Li
Li, Ming
Li, Lei
Shen, Shuqian
author_sort Wang, Jing
collection PubMed
description Since two quantum states that are local unitary (LU) equivalent have the same amount of entanglement, it is meaningful to find a practical method to determine the LU equivalence of given quantum states. In this paper, we present a valid process to find the unitary tensor product decomposition for an arbitrary unitary matrix. Then, by using this process, the conditions for determining the local unitary equivalence of quantum states are obtained. A numerical verification is carried out, which shows the practicability of our protocol. We also present a property of LU invariants by using the universality of quantum gates which can be used to construct the complete set of LU invariants.
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spelling pubmed-104529902023-08-26 Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices Wang, Jing Liu, Xiaoqi Xu, Li Li, Ming Li, Lei Shen, Shuqian Entropy (Basel) Article Since two quantum states that are local unitary (LU) equivalent have the same amount of entanglement, it is meaningful to find a practical method to determine the LU equivalence of given quantum states. In this paper, we present a valid process to find the unitary tensor product decomposition for an arbitrary unitary matrix. Then, by using this process, the conditions for determining the local unitary equivalence of quantum states are obtained. A numerical verification is carried out, which shows the practicability of our protocol. We also present a property of LU invariants by using the universality of quantum gates which can be used to construct the complete set of LU invariants. MDPI 2023-07-29 /pmc/articles/PMC10452990/ /pubmed/37628169 http://dx.doi.org/10.3390/e25081139 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Jing
Liu, Xiaoqi
Xu, Li
Li, Ming
Li, Lei
Shen, Shuqian
Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title_full Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title_fullStr Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title_full_unstemmed Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title_short Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices
title_sort local unitary equivalence of quantum states based on the tensor decompositions of unitary matrices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10452990/
https://www.ncbi.nlm.nih.gov/pubmed/37628169
http://dx.doi.org/10.3390/e25081139
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