{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:57HRQDDTQI6D6NANWVSLAX3FSR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"37c0d5657e348100d5ab00646fa6bba574766c3d9a45f4a7fd1ca91559c287a6","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-06T19:29:12Z","title_canon_sha256":"016e9212b7cbc37196a968448efcb78b1ef382a6a002216647a3bf61da21ffa5"},"schema_version":"1.0","source":{"id":"1206.1307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1307","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1307v1","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1307","created_at":"2026-05-18T03:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"57HRQDDTQI6D","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"57HRQDDTQI6D6NAN","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"57HRQDDT","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:11ef31b6c4b6153955f2c622588ee0c4c482079a465d3f7c198800351e7dd2d1","target":"graph","created_at":"2026-05-18T03:54:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification ","authors_text":"Andreas Winter, Jianxin Chen","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-06T19:29:12Z","title":"Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1307","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fbe55d6765def38bf19c0db50a720b6990cabeed2b4078e2511fb3756d640ca1","target":"record","created_at":"2026-05-18T03:54:06Z","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":"37c0d5657e348100d5ab00646fa6bba574766c3d9a45f4a7fd1ca91559c287a6","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-06T19:29:12Z","title_canon_sha256":"016e9212b7cbc37196a968448efcb78b1ef382a6a002216647a3bf61da21ffa5"},"schema_version":"1.0","source":{"id":"1206.1307","kind":"arxiv","version":1}},"canonical_sha256":"efcf180c73823c3f340db564b05f65944f2f6cca89bc87cefc8d5921cebca950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efcf180c73823c3f340db564b05f65944f2f6cca89bc87cefc8d5921cebca950","first_computed_at":"2026-05-18T03:54:06.477493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:06.477493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hG09G6Yxs6EXe8f7oItQK2fi5uNB4AI5o2ISnPStSVoTRnmDjbFV6fH78Sb2JmQCnhMceSImootNZjCvoa4vDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:06.478146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbe55d6765def38bf19c0db50a720b6990cabeed2b4078e2511fb3756d640ca1","sha256:11ef31b6c4b6153955f2c622588ee0c4c482079a465d3f7c198800351e7dd2d1"],"state_sha256":"0ab31c011bda16c8a532065ae627b7d795dc86d4a353eedcc63106d3845f85c5"}