Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set - Jinli Xu; Baodong Zheng; Hongmei Yao (Journal of Function Spaces and Applications)
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.