{"paper":{"title":"Genuinely multipartite entangled states and orthogonal arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dardo Goyeneche, Karol Zyczkowski","submitted_at":"2014-04-14T14:04:46Z","abstract_excerpt":"A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, written k-uniform, if all its reductions to k qudits are maximally mixed. These states form a natural generalization of N-qudits GHZ states which belong to the class 1-uniform states. We establish a link between the combinatorial notion of orthogonal arrays and k-uniform states and prove the existence of several new classes of such states for N-qudit systems. In particular, known Hadamard matrices allow us to explicitly construct 2-uniform states for an arbitrary number of N>5 qubits. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3586","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"}