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Let Hn be the set of n×n complex Hermitian matrices and n (resp., n) be the set of all idempotent (resp., tripotent) matrices in Hn. In l-partite quantum system Hm1Tml=⊗1lHmi, ⊗1lmi (resp., ⊗1lmi) denotes the set of all decomposable elements ⊗1lAi such that Ai∈mi (resp., Ai∈mi). In this paper, linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1lmi∈n are characterized. As its application, the structure of linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1lmi∈n is also obtained

Linear Transformations between Multipartite Quantum Systems That Map the Set of Tensor Product of Idempotent Matrices into Idempotent Matrix Set