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Counterexample to an additivity conjecture for output purity of quantum channels.Journal of Mathematical Physics, 43(9):4353–4357, 2002","work_id":"f3424188-16ad-4e17-bb0a-bf7384be64d9","year":2002}],"snapshot_sha256":"6101204c39581174df9f7c0e9b61ded1ffc7d2a5ffd8a5022cfe57a438da2144"},"source":{"id":"2605.15439","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T14:44:04.551487Z","id":"040f44e3-3ded-4c91-9a37-34e3556e8332","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves that υ₂(Ω) is multiplicative for CP maps satisfying N† ∘ N = a id + b Tr[·]I, including depolarizing and transpose-depolarizing channels, implying additivity of Rényi-2 entanglement of purification.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A simple algebraic condition on quantum maps makes the Rényi-2 entanglement of purification additive.","strongest_claim":"Whenever a completely positive map N:L(B')→L(A) satisfies N† ∘ N = a id_A + b Tr[·] I_d for constants a,b ≥ 0, the quantity υ₂(N) is multiplicative under tensor powers; this implies additivity for the associated Rényi-2 entanglement of purification.","weakest_assumption":"The reformulation of the Rényi entanglement of purification as the constrained maximal output Schatten p-norm problem (for p=2) is equivalent to the original definition and preserves the relevant multiplicativity properties."}},"verdict_id":"040f44e3-3ded-4c91-9a37-34e3556e8332"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:66902caec1d03fc0dada5cd1568b8542483299130c2358ca6195a8ff82d73bb8","target":"record","created_at":"2026-05-20T00:00:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7dc1be3dab84149465bdd8d114034adbb019f633da3f7c9bc3fad755b23b635c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-14T21:41:31Z","title_canon_sha256":"171ed99c43984e256b1a138673220b7c5d61ea7c3e100d77b7667b2da7b48bc3"},"schema_version":"1.0","source":{"id":"2605.15439","kind":"arxiv","version":1}},"canonical_sha256":"23bc520c2209a5aceeb1d1e8ebbbb4e90d91405a8e6690b6ca3813d109cce031","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23bc520c2209a5aceeb1d1e8ebbbb4e90d91405a8e6690b6ca3813d109cce031","first_computed_at":"2026-05-20T00:00:58.626788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:58.626788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4oJ3hk2tT6shpnALLfPN4Lq0JnahMpX5flZlnMXWtxAAA3QNs8nX8+4B0y++WBlBdRCBsoDq+fJrHHohevGdAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:58.627486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66902caec1d03fc0dada5cd1568b8542483299130c2358ca6195a8ff82d73bb8","sha256:c0e392618219a1b93e3151a9aef026ed24463ede9acb2cd886d78d0d69597625"],"state_sha256":"de5b10cec6e1c85e7bc934657de72dfc35951f57434a4f9824b2351d49aba163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tqV+zK+maZkH4qhi75yth/5jc295smExlOza6+a9pZUMXNYEKy4HudKBj/M3eUEWPkjr54zFicP9tjT6kNo1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:42:52.116678Z","bundle_sha256":"d0aa0369c0fc01b2dc5c812dbad733a522fc53d77b948d072c55439414902fa1"}}