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...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/8/1139 |
| _version_ | 1797584837450661888 |
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| author | Jing Wang Xiaoqi Liu Li Xu Ming Li Lei Li Shuqian Shen |
| author_facet | Jing Wang Xiaoqi Liu Li Xu Ming Li Lei Li Shuqian Shen |
| author_sort | Jing Wang |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T23:58:23Z |
| format | Article |
| id | doaj.art-809637c3c6014cee98f1915065f47449 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T23:58:23Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-809637c3c6014cee98f1915065f474492023-11-19T00:59:07ZengMDPI AGEntropy1099-43002023-07-01258113910.3390/e25081139Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary MatricesJing Wang0Xiaoqi Liu1Li Xu2Ming Li3Lei Li4Shuqian Shen5College of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaCollege of Science, China University of Petroleum, Qingdao 266580, ChinaSince 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.https://www.mdpi.com/1099-4300/25/8/1139local unitary equivalencequantum statesquantum entanglement |
| spellingShingle | Jing Wang Xiaoqi Liu Li Xu Ming Li Lei Li Shuqian Shen Local Unitary Equivalence of Quantum States Based on the Tensor Decompositions of Unitary Matrices Entropy local unitary equivalence quantum states quantum entanglement |
| 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 | local unitary equivalence quantum states quantum entanglement |
| url | https://www.mdpi.com/1099-4300/25/8/1139 |
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