{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BKX3TOLKIKQUU3LUDJH6IH3RCL","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":"b02d17bda0bcabf8c33b3e7c8a52785836f84de8c711e75067a3de677256d0bb","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-07T15:46:16Z","title_canon_sha256":"268236757d5c6e18bd6ea612cd7d4e846fb3cff00042621b6f9f56b65e01235a"},"schema_version":"1.0","source":{"id":"1208.1449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1449","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1449v1","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1449","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"BKX3TOLKIKQU","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BKX3TOLKIKQUU3LU","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BKX3TOLK","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:496a3260a5cca58ac7b80c30a44f60a301679d38895c00fc22b006b2e25eef04","target":"graph","created_at":"2026-05-17T23:52:44Z","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":"In this paper, we study the behaviour of the output of pure entangled states after being transformed by a product of conjugate random unitary channels. This study is motivated by the counterexamples by Hastings and Hayden-Winter to the additivity problems. In particular, we study in depth the difference of behaviour between random unitary channels and generic random channels. In the case where the number of unitary operators is fixed, we compute the limiting eigenvalues of the output states. In the case where the number of unitary operators grows linearly with the dimension of the input space,","authors_text":"Benoit Collins, Ion Nechita, Motohisa Fukuda","cross_cats":["math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-07T15:46:16Z","title":"Low entropy output states for products of random unitary channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1449","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":"sha256:0b167c812dbc8c4d99479dc455c972af8e0579dd92d79cc370bbb77543cad5ad","target":"record","created_at":"2026-05-17T23:52:44Z","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":"b02d17bda0bcabf8c33b3e7c8a52785836f84de8c711e75067a3de677256d0bb","cross_cats_sorted":["math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-07T15:46:16Z","title_canon_sha256":"268236757d5c6e18bd6ea612cd7d4e846fb3cff00042621b6f9f56b65e01235a"},"schema_version":"1.0","source":{"id":"1208.1449","kind":"arxiv","version":1}},"canonical_sha256":"0aafb9b96a42a14a6d741a4fe41f7112c33b8f7d71d6d8038b2285504524d0d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aafb9b96a42a14a6d741a4fe41f7112c33b8f7d71d6d8038b2285504524d0d2","first_computed_at":"2026-05-17T23:52:44.920518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:44.920518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucfegg1TW3Q4ko+QZXZbGAeKnvLvrzmCmtW/g7Cs3UoVOaGfP1pafbh13Nmbm8jAOqMGrfJY5a6wvALzu2WJAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:44.921018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b167c812dbc8c4d99479dc455c972af8e0579dd92d79cc370bbb77543cad5ad","sha256:496a3260a5cca58ac7b80c30a44f60a301679d38895c00fc22b006b2e25eef04"],"state_sha256":"f2cb6863137a904a692c0528dd9a435bb5bf9177666403b84c14a9a281933bc5"}