{"paper":{"title":"Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J. Solomon Ivan, Krishna Kumar Sabapathy, R. Simon","submitted_at":"2017-05-19T15:16:21Z","abstract_excerpt":"Continuous-variable systems in quantum theory can be fully described through any one of the ${\\rm s}$-ordered family of quasiprobabilities $\\Lambda_{\\rm s}(\\alpha)$, ${\\rm s} \\in [-1,1]$. We ask for what values of $({\\rm s}, a)$ is the scaling map $\\Lambda_{\\rm s}(\\alpha) \\rightarrow a^{-2} \\Lambda_{\\rm s}(a^{-1}\\alpha)$ a positive map? Our analysis based on a duality we establish settles this issue (i) the scaling map generically fails to be positive, showing that there is no useful entanglement witness of the scaling type beyond the transpose map, and (ii) in the two particular cases $({\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07044","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"}