{"paper":{"title":"A common algebraic description for probabilistic and quantum computations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jose M. Fernandez, Markus Holzer, Martin Beaudry","submitted_at":"2002-12-16T22:37:51Z","abstract_excerpt":"We study the computational complexity of the problem SFT (Sum-free Formula partial Trace): given a tensor formula F over a subsemiring of the complex field (C,+,.) plus a positive integer k, under the restrictions that all inputs are column vectors of L2-norm 1 and norm-preserving square matrices, and that the output matrix is a column vector, decide whether the k-partial trace of $F\\dagg{F}$ is superior to 1/2. The k-partial trace of a matrix is the sum of its lowermost k diagonal elements. We also consider the promise version of this problem, where the 1/2 threshold is an isolated cutpoint. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0212096","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"}