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

Abstract EN

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, ⊗1l?mi (resp., ⊗1l?mi) 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⊗1l?mi∈?n are characterized.

As its application, the structure of linear maps ϕ from Hm1⋯ml to Hn with n≤m1⋯ml such that ϕ⊗1l?mi∈?n is also obtained.