{"paper":{"title":"Limit Theorems for the Discrete-Time Quantum Walk on a Graph with Joined Half Lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Etsuo Segawa, Kota Chisaki, Norio Konno","submitted_at":"2010-09-07T14:29:47Z","abstract_excerpt":"We consider a discrete-time quantum walk $W_{t,\\kappa}$ at time $t$ on a graph with joined half lines $\\mathbb{J}_\\kappa$, which is composed of $\\kappa$ half lines with the same origin. Our analysis is based on a reduction of the walk on a half line. The idea plays an important role to analyze the walks on some class of graphs with \\textit{symmetric} initial states. In this paper, we introduce a quantum walk with an enlarged basis and show that $W_{t,\\kappa}$ can be reduced to the walk on a half line even if the initial state is \\textit{asymmetric}. For $W_{t,\\kappa}$, we obtain two types of l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1306","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"}