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We answer it in the negative. To this end, we show the following stronger statement: for all $C\\in M_{d_1d_2}(\\mathbb{C})$ of rank at most $r \\le d_1 d_2$, $\\mathrm{tr}_1(C)\\|_F^2+\\|\\mathrm{tr}_2(C)\\|_F^2 \\le r\\|C\\|_F^2+\\frac{1}{r}|\\mathrm{tr}(C)|^2$. A result by Costa Rico on the equivalence of this inequality with two-copy undistillability at $r = 2$ "},"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":"2607.24309","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-27T11:51:18Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"5d3fe1cfa7bff27c236f57e7290d2e84bbfd30f25ca84d357e662e70c9cd06d8","abstract_canon_sha256":"e9aaedef72607a169d357021b7ae308e4b0f551d314932c94bdb48173cf26d39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:23:56.675999Z","signature_b64":"LdmzKoayMm+D+TzQFgIvaj15fuY+fxjegI7H1y4mVEkEfC9vp5amadgorSRgDFUrruIFBtkRwixw7Dy4Wtv2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed5df8d321d6a8fd3abcc8088baa2fb9102eab46eb95f6d3cc9dd31e44b3961","last_reissued_at":"2026-07-28T02:23:56.675134Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:23:56.675134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the two-copy distillability of Werner states and a new partial trace inequality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"quant-ph","authors_text":"Bal\\'azs Pozsgay, Felix Huber, Istv\\'an Vona, Thomas C. Fraser","submitted_at":"2026-07-27T11:51:18Z","abstract_excerpt":"Problem 5 in {\\it Five Open Problems in Quantum Information Theory} [PRX Quantum 3, 010101 (2022)], asks whether the two-ququart Werner state $\\varrho(4,-\\tfrac12)$ is two-copy distillable, where $\\varrho(d,\\alpha)=(I+\\alpha F)/(d^2+\\alpha d)$. We answer it in the negative. To this end, we show the following stronger statement: for all $C\\in M_{d_1d_2}(\\mathbb{C})$ of rank at most $r \\le d_1 d_2$, $\\mathrm{tr}_1(C)\\|_F^2+\\|\\mathrm{tr}_2(C)\\|_F^2 \\le r\\|C\\|_F^2+\\frac{1}{r}|\\mathrm{tr}(C)|^2$. A result by Costa Rico on the equivalence of this inequality with two-copy undistillability at $r = 2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24309","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/2607.24309/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.24309","created_at":"2026-07-28T02:23:56.675580+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.24309v1","created_at":"2026-07-28T02:23:56.675580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24309","created_at":"2026-07-28T02:23:56.675580+00:00"},{"alias_kind":"pith_short_12","alias_value":"53K57DJSDVVI","created_at":"2026-07-28T02:23:56.675580+00:00"},{"alias_kind":"pith_short_16","alias_value":"53K57DJSDVVI7U5L","created_at":"2026-07-28T02:23:56.675580+00:00"},{"alias_kind":"pith_short_8","alias_value":"53K57DJS","created_at":"2026-07-28T02:23:56.675580+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O","json":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O.json","graph_json":"https://pith.science/api/pith-number/53K57DJSDVVI7U5LZSAIROVC7O/graph.json","events_json":"https://pith.science/api/pith-number/53K57DJSDVVI7U5LZSAIROVC7O/events.json","paper":"https://pith.science/paper/53K57DJS"},"agent_actions":{"view_html":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O","download_json":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O.json","view_paper":"https://pith.science/paper/53K57DJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.24309&json=true","fetch_graph":"https://pith.science/api/pith-number/53K57DJSDVVI7U5LZSAIROVC7O/graph.json","fetch_events":"https://pith.science/api/pith-number/53K57DJSDVVI7U5LZSAIROVC7O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O/action/storage_attestation","attest_author":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O/action/author_attestation","sign_citation":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O/action/citation_signature","submit_replication":"https://pith.science/pith/53K57DJSDVVI7U5LZSAIROVC7O/action/replication_record"}},"created_at":"2026-07-28T02:23:56.675580+00:00","updated_at":"2026-07-28T02:23:56.675580+00:00"}