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 ℘n (resp.,tn) be the set of all idempotent (resp.,tripotent) matrices in hn. in l -partite quantum system h m1⋯tml = ⊗ 1/l hmi,⊗ 1/l ℘mi (resp.,⊗ 1*l tmi) denotes the set of all decomposable elements ⊗ 1/l ai such that a i ∈ ℘mi (resp.,ai ∈ tmi). in this paper,linear maps φ from hm1⋯ml to hn with n ≤ m1⋯ml such that φ ⊗ 1/l ℘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 ⊗ 1/l tmi ∈ tn is also obtained. © 2013 jinli xu et al.