{"paper":{"title":"Sinkhorn-Knopp Theorem for PPT states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.OA","authors_text":"Daniel Cariello","submitted_at":"2018-07-15T19:35:20Z","abstract_excerpt":"Given a PPT state $A=\\sum_{i=1}^nA_i\\otimes B_i \\in M_k\\otimes M_k$ and a vector $v\\in\\Im(A)\\subset\\mathbb{C}^k\\otimes\\mathbb{C}^k$ with tensor rank $k$, we provide an algorithm that checks whether the positive map $G_A:M_k\\rightarrow M_k$, $G_A(X)=\\sum_{i=1}^n tr(A_iX)B_i$, is equivalent to a doubly stochastic map. This procedure is based on the search for Perron eigenvectors of completely positive maps and unique solutions of, at most, $k$ unconstrained quadratic minimization problems. As a corollary, we can check whether this state can be put in the filter normal form. This normal form is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06955","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"}