Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set
Let Hn be the set of n×n complex Hermitian matrices and 𝒫n (resp., 𝒯n) be the set of all idempotent (resp., tripotent) matrices in Hn. In l-partite quantum system Hm1Tml=⊗1lHmi, ⊗1l𝒫mi (resp., ⊗1l𝒯mi) denotes the set of all decomposable elements ⊗1lAi such that Ai∈𝒫mi (resp., Ai∈𝒯mi). In this paper,...
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| Format: | Article |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/182569 |
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| author | Jinli Xu Baodong Zheng Hongmei Yao |
| author_facet | Jinli Xu Baodong Zheng Hongmei Yao |
| author_sort | Jinli Xu |
| collection | DOAJ |
| description | Let Hn be the set of n×n complex Hermitian matrices and 𝒫n (resp., 𝒯n) be the set of all idempotent (resp., tripotent) matrices in Hn. In l-partite quantum system Hm1Tml=⊗1lHmi, ⊗1l𝒫mi (resp., ⊗1l𝒯mi) denotes the set of all decomposable elements ⊗1lAi such that Ai∈𝒫mi (resp., Ai∈𝒯mi). In this paper, linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1l𝒫mi∈𝒫n are characterized. As its application, the structure of linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1l𝒯mi∈𝒯n is also obtained. |
| format | Article |
| id | doaj-art-7036258bb36b4bc58a093e0c62a6c522 |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
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| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7036258bb36b4bc58a093e0c62a6c5222025-08-20T02:06:46ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/182569182569Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix SetJinli Xu0Baodong Zheng1Hongmei Yao2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaCollege of Science, Harbin Engineering University, Harbin 150001, ChinaLet Hn be the set of n×n complex Hermitian matrices and 𝒫n (resp., 𝒯n) be the set of all idempotent (resp., tripotent) matrices in Hn. In l-partite quantum system Hm1Tml=⊗1lHmi, ⊗1l𝒫mi (resp., ⊗1l𝒯mi) denotes the set of all decomposable elements ⊗1lAi such that Ai∈𝒫mi (resp., Ai∈𝒯mi). In this paper, linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1l𝒫mi∈𝒫n are characterized. As its application, the structure of linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1l𝒯mi∈𝒯n is also obtained.http://dx.doi.org/10.1155/2013/182569 |
| spellingShingle | Jinli Xu Baodong Zheng Hongmei Yao Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set Journal of Function Spaces and Applications |
| title | Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set |
| title_full | Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set |
| title_fullStr | Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set |
| title_full_unstemmed | Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set |
| title_short | Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set |
| title_sort | linear transformations between multipartite quantum systems that map the set of tensor product of idempotent matrices into idempotent matrix set |
| url | http://dx.doi.org/10.1155/2013/182569 |
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