{"paper":{"title":"Absorption Probabilities of Quantum Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Mark Kon, Parker Kuklinski","submitted_at":"2019-05-10T16:14:17Z","abstract_excerpt":"Quantum walks are known to have nontrivial interaction with absorbing boundaries. In particular, Ambainis et.\\ al.\\ \\cite{ambainis01} showed that in the $(\\Z ,C_1,H)$ quantum walk (one-dimensional Hadamard walk) an absorbing boundary partially reflects information. These authors also conjectured that the left absorption probabilities $P_n^{(1)}(1,0)$ related to the finite absorbing Hadamard walks $(\\Z ,C_1,H,\\{ 0,n\\} )$ satisfy a linear fractional recurrence in $n$ (here $P_n(1,0)$ is the probability that a Hadamard walk particle initialized in $|1\\rangle |R\\rangle$ is eventually absorbed at $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04239","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"}