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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.02590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-03T17:57:15Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"33d3d35b0e3ddbb621164085fc019664dfb9940f4f03061cf40cf1205135dcb8","abstract_canon_sha256":"15bdbca9eb35cf9110511bf56d8e30f7bc369c9e41c77256b99646926168f1e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:44:19.742371Z","signature_b64":"S+YRcEJWPqpuobsdIjgmKxCHURn37raOK1o3LwkhyxNgFaPQdQGqRUma4u7QE1blGEbYKpH6oQfbz8gYlWfoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc78150c4f23c1237dc020f61d1518c47279b9dd7eced97cc17b44acbd37c087","last_reissued_at":"2026-08-04T02:44:19.740079Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:44:19.740079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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). 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