{"paper":{"title":"Universal State Transfer on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Christino Tamon, Leah Granger, Oliver Hennigh, Shannon Fehrenbach, Stephen Cameron, Sunrose Shrestha","submitted_at":"2013-10-15T00:10:21Z","abstract_excerpt":"A continuous-time quantum walk on a graph $G$ is given by the unitary matrix $U(t) = \\exp(-itA)$, where $A$ is the Hermitian adjacency matrix of $G$. We say $G$ has pretty good state transfer between vertices $a$ and $b$ if for any $\\epsilon > 0$, there is a time $t$, where the $(a,b)$-entry of $U(t)$ satisfies $|U(t)_{a,b}| \\ge 1-\\epsilon$. This notion was introduced by Godsil (2011). The state transfer is perfect if the above holds for $\\epsilon = 0$. In this work, we study a natural extension of this notion called universal state transfer. Here, state transfer exists between every pair of v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3885","kind":"arxiv","version":1},"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"}