{"paper":{"title":"Hierarchy of Spin Operators, Quantum Gates, Entanglement, Tensor Product and Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Willi-Hans Steeb, Yorick Hardy","submitted_at":"2015-09-26T09:25:47Z","abstract_excerpt":"{\\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit the same spectrum. Both Hamilton operators play a central role for quantum gates in particular for the case spin-$\\frac12$ and the case spin-1. The spin-$\\frac12$, spin-1, spin-$\\frac32$ and spin-2 cases are studied in detail. Entanglement and mutually unbiased bases of the eigenvectors is discussed. Two triple Hamilton operators are also investigated. Both are also admitting the same spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07955","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"}