Merging of positive maps: a construction of various classes of positive maps on matrix algebras
Marcin Marciniak, Adam Rutkowski

TL;DR
This paper introduces a method to construct new positive maps on matrix algebras by merging existing maps, providing conditions for their positivity and revealing new classes of exposed positive maps with applications to entangled PPT states.
Contribution
It presents a novel merging construction for positive maps, establishing conditions for various positivity properties and identifying new classes of exposed positive maps.
Findings
Nondecomposable merging of 2-positive and 2-copositive maps
Canonical merging of extremal maps yields exposed positive maps
Application to constructing entangled PPT states
Abstract
For two positive maps , , we construct a new linear map , where , , by means of some additional ingredients such as operators and functionals. We call it a merging of maps and . We discuss properties of this construction. In particular, we provide conditions for positivity of , as well as for -positivity, complete positivity and nondecomposability. In particular, we show that for a pair composed of -positive and -copositive maps, there is a nondecomposable 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…
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