Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773269 | Linear Algebra and its Applications | 2017 | 43 Pages |
Abstract
For two positive maps Ïi:B(Ki)âB(Hi), i=1,2, we construct a new linear map Ï:B(H)âB(K), where K=K1âK2âC, H=H1âH2âC, by means of some additional ingredients such as operators and functionals. We call it a merging of maps Ï1 and Ï2. The properties of this construction are discussed. In particular, conditions for positivity of Ï, 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marcin Marciniak, Adam Rutkowski,