{"paper":{"title":"Catalytic majorization and $\\ell_p$ norms","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Guillaume Aubrun (ICJ), Ion Nechita (ICJ)","submitted_at":"2007-02-15T12:48:57Z","abstract_excerpt":"An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local operations and classical communication) ? Mathematically, the question amounts to describe, for a fixed vector $y$, the set $T(y)$ of vectors $x$ such that we have $x \\otimes z \\prec y \\otimes z$ for some $z$, where $\\prec$ denotes the standard majorization relation. Our main result is that the closure of $T(y)$ in the $\\ell_1$ norm can be fully d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0702153","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"}