{"paper":{"title":"Real State Transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Godsil","submitted_at":"2017-10-11T12:55:36Z","abstract_excerpt":"A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is specified by the 1-parameter family of unitary matrices $U(t)=\\exp(itA)$. These matrices act on the state space of a quantum system, the states of which we may represent by density matrices, positive semidefinite matrices with rows and columns indexed by $V(X)$ and with trace $1$. The square of the absolute values of the entries of a column of $U(t)$ define a probability density on $V(X)$, and it is precisely these densities that predict the outcomes of measurements. There are two special cases of physical interest: when the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04042","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"}