{"paper":{"title":"Merging of positive maps: a construction of various classes of positive maps on matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OA","authors_text":"Adam Rutkowski, Marcin Marciniak","submitted_at":"2016-05-07T17:30:43Z","abstract_excerpt":"For two positive maps $\\phi_i:B(\\mathcal{K}_i)\\to B(\\mathcal{H}_i)$, $i=1,2$, we construct a new linear map $\\phi:B(\\mathcal{H})\\to B(\\mathcal{K})$, where $\\mathcal{K}=\\mathcal{K}_1\\oplus\\mathcal{K}_2\\oplus\\mathbb{C}$, $\\mathcal{H}=\\mathcal{H}_1\\oplus\\mathcal{H}_2\\oplus\\mathbb{C}$, by means of some additional ingredients such as operators and functionals. We call it a merging of maps $\\phi_1$ and $\\phi_2$. We discuss properties of this construction. In particular, we provide conditions for positivity of $\\phi$, as well as for $2$-positivity, complete positivity and nondecomposability. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02219","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}