{"paper":{"title":"Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jon Tyson","submitted_at":"2002-10-13T19:11:01Z","abstract_excerpt":"Operator-Schmidt decompositions of the quantum Fourier transform on C^N1 tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1>N2. The first known special case, N1=N2=2^n, was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0210100","kind":"arxiv","version":3},"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"}