Article ID Journal Published Year Pages File Type
5773269 Linear Algebra and its Applications 2017 43 Pages PDF
Abstract
For two positive maps ϕi:B(Ki)→B(Hi), i=1,2, we construct a new linear map ϕ:B(H)→B(K), where K=K1⊕K2⊕C, H=H1⊕H2⊕C, by means of some additional ingredients such as operators and functionals. We call it a merging of maps ϕ1 and ϕ2. The properties of this construction are discussed. In particular, conditions for positivity of ϕ, as well as for 2-positivity, complete positivity, optimality and indecomposability, are provided. In particular, we show that for a pair composed of 2-positive and 2-copositive maps, there is an indecomposable merging of them. One of our main results asserts, that for a canonical merging of a pair composed of completely positive and completely copositive extremal maps, their canonical merging is an exposed positive map. This result provides a wide class of new examples of exposed positive maps. As an application, new examples of entangled PPT states are described.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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