保持算子张量积凸组合的非线性映射

Nonlinear Maps Preserving Convex Combination of Tensor Products of Operators

本文给出保持凸组合的可分二体态之间非线性双射的结构性质,证明了此类映射Φ在一定的条件下具有形式Φ(ρσ)=(ST)Ψ(ρσ)(ST)*Tr((ST)Ψ(ρσ)(ST)*).其中,Ψ是恒等映射,或转置,或对第一个张量因子取偏转置,或对第二个张量因子取偏转置,或上述映射与交换映射(swap)的复合。

In this paper,we give a structure feature of convex combination preserving bijective maps which send separable states to separable states of bipartite system. It is shown that such a map φ has the form of φ（ρ⊕б）=（S⊕T）ψ（ρ⊕б）（S⊕T）^./Tr（（S⊕T）ψ（ρ⊕б）（S⊕T）^.where φ is one of the identity,transpose, partial transpose,or a combination of above mentioned map with the swap.