{"paper":{"title":"Limit theorems for discrete-time quantum walks on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Etsuo Segawa, Kota Chisaki, Masatoshi Hamada, Norio Konno","submitted_at":"2009-03-26T06:16:39Z","abstract_excerpt":"We consider a discrete-time quantum walk W_t given by the Grover transformation on the Cayley tree. We reduce W_t to a quantum walk X_t on a half line with a wall at the origin. This paper presents two types of limit theorems for X_t. The first one is X_t as t\\to\\infty, which corresponds to a localization in the case of an initial qubit state. The second one is X_t/t as t\\to\\infty, whose limit density is given by the Konno density function [1-4]. The density appears in various situations of discrete-time cases. The corresponding similar limit theorem was proved in [5] for a continuous-time cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4508","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"}