{"paper":{"title":"Characterization of circulant graphs having perfect state transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"cs.DM","authors_text":"Milan Ba\\v{s}i\\'c","submitted_at":"2011-04-11T01:24:53Z","abstract_excerpt":"In this paper we answer the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer. The network is described by a circulant graph $G$, which is characterized by its circulant adjacency matrix $A$. Formally, we say that there exists a {\\it perfect state transfer} (PST) between vertices $a,b\\in V(G)$ if $|F(\\tau)_{ab}|=1$, for some positive real number $\\tau$, where $F(t)=\\exp(\\i At)$. Saxena, Severini and Shparlinski ({\\it International Journal of Quantum Information} 5 (2007), 417--430) proved that $|F(\\tau)_{aa}|=1$ for some $a\\in V(G)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1825","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"}