{"paper":{"title":"Perfect quantum state transfer on the Johnson scheme","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Mokhtar, Bahman Ahmadi, M. H. Shirdareh Haghighi","submitted_at":"2017-10-25T07:45:24Z","abstract_excerpt":"For any graph $X$ with the adjacency matrix $A$, the transition matrix of the continuous-time quantum walk at time $t$ is given by the matrix-valued function $\\mathcal{H}_X(t)=\\mathrm{e}^{itA}$. We say that there is perfect state transfer in $X$ from the vertex $u$ to the vertex $v$ at time $\\tau$ if $|\\mathcal{H}_X(\\tau)_{u,v}| = 1$. It is an important problem to determine whether perfect state transfers can happen on a given family of graphs. In this paper we characterize all the graphs in the Johnson scheme which have this property. Indeed, we show that the Kneser graph $K(2k,k)$ is the onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09096","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"}