Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set. (12th August 2013) - Xu, Jinli; Zheng, Baodong; Yao, Hongmei
Abstract : Let H n be the set of n × n complex Hermitian matrices and 𝒫 n (resp., 𝒯 n ) be the set of all idempotent (resp., tripotent) matrices in H n . In l -partite quantum system H m 1 T m l = ⊗ 1 l H m i, ⊗ 1 l 𝒫 m i (resp., ⊗ 1 l 𝒯 m i ) denotes the set of all decomposable elements ⊗ 1 l A i such that A i ∈ 𝒫 m i (resp., A i ∈ 𝒯 m i ). In this paper, linear maps ϕ from H m 1 ⋯ m l to H n with n ≤ m 1 ⋯ m l such that ϕ ⊗ 1 l 𝒫 m i ∈ 𝒫 n are characterized. As its application, the structure of linear maps ϕ from H m 1 ⋯ m l to H n with n ≤ m 1 ⋯ m l such that ϕ ⊗ 1 l 𝒯 m i ∈ 𝒯 n is also obtained.