{"paper":{"title":"Optimal Quantum de Finetti Theorems via Argmax Rounding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Fernando Granha Jeronimo, Haochen Xu, Pei Wu","submitted_at":"2026-08-03T17:57:15Z","abstract_excerpt":"We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $\\rho_N\\in D(\\mathrm{Sym}^N(\\mathbb C^d))$, there is a probability measure $\\nu$ on the unit sphere such that \\[\n  \\left\\|\n  \\rho_N^{(2)}-\\int |u\\rangle\\langle u|^{\\otimes 2}\\,d\\nu(u)\n  \\right\\|_1\n  \\le \\frac{\\sqrt{d-1}}{N-1}. \\] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchangeable states. These results settle the dimension dependence left open by Christandl, K\\\"onig, Mitchison, and Renner (CMP 2007). The proof casts de Finetti approximation as sum-of-squares ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02590","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.02590/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}