{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W4CHA2LI7TRWCMGBB5GSTUPGCZ","short_pith_number":"pith:W4CHA2LI","canonical_record":{"source":{"id":"1305.1567","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-07T16:09:29Z","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"title_canon_sha256":"fa1615a0482921f4252da824715f22ecc4982d6afd08d240849b5f297962450f","abstract_canon_sha256":"36427bb6b8f512dc43ffbc6a8ef791b3c530e497f374b579e0a00587bd9a915e"},"schema_version":"1.0"},"canonical_sha256":"b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347","source":{"kind":"arxiv","id":"1305.1567","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1567","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1567v3","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1567","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"W4CHA2LI7TRW","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W4CHA2LI7TRWCMGB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W4CHA2LI","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W4CHA2LI7TRWCMGBB5GSTUPGCZ","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1567","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-07T16:09:29Z","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"title_canon_sha256":"fa1615a0482921f4252da824715f22ecc4982d6afd08d240849b5f297962450f","abstract_canon_sha256":"36427bb6b8f512dc43ffbc6a8ef791b3c530e497f374b579e0a00587bd9a915e"},"schema_version":"1.0"},"canonical_sha256":"b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.274954Z","signature_b64":"ZeiC2+MMXFQZdOJQmGHL4gy3jf1s1h5b4B5Hpu2lQmBSP+sRntFjHy5vvZN9MDVINs5WeOK80HJtKPCwOfA+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347","last_reissued_at":"2026-05-18T01:06:23.274465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.274465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1567","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBrQC46wPrjf5tJCp9Ds7gSZdlsxZJZISEKf5XeEgBOw1Ys5gm1PzdcX1G7Z3+Yl4/EDxZ7LZ5CN2XowKYXgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:36:47.477621Z"},"content_sha256":"0682d74dab2ba284ef7bd057bf02e9eeb22d0f83b645c77266f972d0e90224f5","schema_version":"1.0","event_id":"sha256:0682d74dab2ba284ef7bd057bf02e9eeb22d0f83b645c77266f972d0e90224f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W4CHA2LI7TRWCMGBB5GSTUPGCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost one bit violation for the additivity of the minimum output entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Benoit Collins, Ion Nechita, Serban T. Belinschi","submitted_at":"2013-05-07T16:09:29Z","abstract_excerpt":"In a previous paper, we proved that the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_{k,t}. We also showed that the set K_{k,t} is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of l^p norms on the set K_{k,t} and prove that the maximum is attained on a vector of shape (a,b,...,b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1567","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+OMq/29Fvbz1vPtCL91/FDwqHDnz8hQXzoWRYiE3xq699EQZuqcWkFVrVBCTlMu7eHhU4PsSOqfbF5F89NzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:36:47.477965Z"},"content_sha256":"537977827f82f27e10b03b4f24ee5de43354674458b086ef848ce0462af2c2b7","schema_version":"1.0","event_id":"sha256:537977827f82f27e10b03b4f24ee5de43354674458b086ef848ce0462af2c2b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/bundle.json","state_url":"https://pith.science/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T01:36:47Z","links":{"resolver":"https://pith.science/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ","bundle":"https://pith.science/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/bundle.json","state":"https://pith.science/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W4CHA2LI7TRWCMGBB5GSTUPGCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W4CHA2LI7TRWCMGBB5GSTUPGCZ","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":"36427bb6b8f512dc43ffbc6a8ef791b3c530e497f374b579e0a00587bd9a915e","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-07T16:09:29Z","title_canon_sha256":"fa1615a0482921f4252da824715f22ecc4982d6afd08d240849b5f297962450f"},"schema_version":"1.0","source":{"id":"1305.1567","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1567","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1567v3","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1567","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"W4CHA2LI7TRW","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W4CHA2LI7TRWCMGB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W4CHA2LI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:537977827f82f27e10b03b4f24ee5de43354674458b086ef848ce0462af2c2b7","target":"graph","created_at":"2026-05-18T01:06:23Z","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 a previous paper, we proved that the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_{k,t}. We also showed that the set K_{k,t} is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of l^p norms on the set K_{k,t} and prove that the maximum is attained on a vector of shape (a,b,...,b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show t","authors_text":"Benoit Collins, Ion Nechita, Serban T. Belinschi","cross_cats":["math.MP","math.OA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-07T16:09:29Z","title":"Almost one bit violation for the additivity of the minimum output entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1567","kind":"arxiv","version":3},"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":"sha256:0682d74dab2ba284ef7bd057bf02e9eeb22d0f83b645c77266f972d0e90224f5","target":"record","created_at":"2026-05-18T01:06:23Z","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":"36427bb6b8f512dc43ffbc6a8ef791b3c530e497f374b579e0a00587bd9a915e","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-07T16:09:29Z","title_canon_sha256":"fa1615a0482921f4252da824715f22ecc4982d6afd08d240849b5f297962450f"},"schema_version":"1.0","source":{"id":"1305.1567","kind":"arxiv","version":3}},"canonical_sha256":"b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b704706968fce36130c10f4d29d1e6164810dba36c92855f761842d2ffe3b347","first_computed_at":"2026-05-18T01:06:23.274465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.274465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZeiC2+MMXFQZdOJQmGHL4gy3jf1s1h5b4B5Hpu2lQmBSP+sRntFjHy5vvZN9MDVINs5WeOK80HJtKPCwOfA+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.274954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1567","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0682d74dab2ba284ef7bd057bf02e9eeb22d0f83b645c77266f972d0e90224f5","sha256:537977827f82f27e10b03b4f24ee5de43354674458b086ef848ce0462af2c2b7"],"state_sha256":"e30c80c34cb1e16a26a2a58208dfefd26e8a024afdf7eb70d81cf09deeefd8b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CiVcMCnDOxVe+cnXPBn9nl78CcnP1EQanX53xHCamep4YGuWJagu4oMs3AhpMHmZdSyecpAvoG95D4KvufpNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:36:47.479920Z","bundle_sha256":"bf110fe6a87ac5d3c94af8730552134bdd132f47d052ed71a0edc1fa190e350d"}}