{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CBOXWGXTERUOAFA6JVREJCA2K2","short_pith_number":"pith:CBOXWGXT","canonical_record":{"source":{"id":"1108.4073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-19T23:19:19Z","cross_cats_sorted":[],"title_canon_sha256":"7e7c6bd06baf3579ef0651ee9f7449fa1e81b4b1f038bedcc68a88d71f209c7d","abstract_canon_sha256":"f2bc514a20ba21d47e425fd636f46208697886d2fdec1d1bc8d945ff2035f91a"},"schema_version":"1.0"},"canonical_sha256":"105d7b1af32468e0141e4d6244881a568a3f9cb16bee36338e32837c28037f08","source":{"kind":"arxiv","id":"1108.4073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4073","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4073v1","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4073","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"CBOXWGXTERUO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CBOXWGXTERUOAFA6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CBOXWGXT","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CBOXWGXTERUOAFA6JVREJCA2K2","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-19T23:19:19Z","cross_cats_sorted":[],"title_canon_sha256":"7e7c6bd06baf3579ef0651ee9f7449fa1e81b4b1f038bedcc68a88d71f209c7d","abstract_canon_sha256":"f2bc514a20ba21d47e425fd636f46208697886d2fdec1d1bc8d945ff2035f91a"},"schema_version":"1.0"},"canonical_sha256":"105d7b1af32468e0141e4d6244881a568a3f9cb16bee36338e32837c28037f08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.917771Z","signature_b64":"zYT4Pc8Fyuet7CdyHyMPRzsBbJvsdRC6UvjMUYD8fRKSWK9IqY62DhuoOzZ4IBX5LEGfQXL0WUkN7bh8USRBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"105d7b1af32468e0141e4d6244881a568a3f9cb16bee36338e32837c28037f08","last_reissued_at":"2026-05-18T02:45:48.917275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.917275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4073","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2GQA9LawNJHtI1KOWKWzsWjMwIT4KkMWQANBMiph5bLoh3wDPcnbOdqbxhAQmrpOhHPvVnqkaMAdDaO3va2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:07:16.270990Z"},"content_sha256":"5e88b78e4313a85f6739d97f6d40c5f03a203f8657a2b3b8af1a388692b0fee7","schema_version":"1.0","event_id":"sha256:5e88b78e4313a85f6739d97f6d40c5f03a203f8657a2b3b8af1a388692b0fee7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CBOXWGXTERUOAFA6JVREJCA2K2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"All maximally entangling unitary gates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Scott M. Cohen","submitted_at":"2011-08-19T23:19:19Z","abstract_excerpt":"We characterize all maximally entangling bipartite unitary operators, acting on systems $A,B$ of arbitrary finite dimensions $d_A\\le d_B$, when use of ancillary systems by both parties is allowed. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when $d_A=d_B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4073","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":""},"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":"2026-05-18T02:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRW65HK/YXVA+lr8CTQIMCJWQ2WF/lq6acCOhhpTKiLJl3YRqd53+MTPZD5SASmp/OggNdvQpMvhV/EvHwPIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:07:16.271338Z"},"content_sha256":"19541d1a53ded67d593b000b9cab476c97cf5ab52d755776e90a5302dd2035ec","schema_version":"1.0","event_id":"sha256:19541d1a53ded67d593b000b9cab476c97cf5ab52d755776e90a5302dd2035ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBOXWGXTERUOAFA6JVREJCA2K2/bundle.json","state_url":"https://pith.science/pith/CBOXWGXTERUOAFA6JVREJCA2K2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBOXWGXTERUOAFA6JVREJCA2K2/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":"2026-07-03T11:07:16Z","links":{"resolver":"https://pith.science/pith/CBOXWGXTERUOAFA6JVREJCA2K2","bundle":"https://pith.science/pith/CBOXWGXTERUOAFA6JVREJCA2K2/bundle.json","state":"https://pith.science/pith/CBOXWGXTERUOAFA6JVREJCA2K2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBOXWGXTERUOAFA6JVREJCA2K2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CBOXWGXTERUOAFA6JVREJCA2K2","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":"f2bc514a20ba21d47e425fd636f46208697886d2fdec1d1bc8d945ff2035f91a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-19T23:19:19Z","title_canon_sha256":"7e7c6bd06baf3579ef0651ee9f7449fa1e81b4b1f038bedcc68a88d71f209c7d"},"schema_version":"1.0","source":{"id":"1108.4073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4073","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4073v1","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4073","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"CBOXWGXTERUO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CBOXWGXTERUOAFA6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CBOXWGXT","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:19541d1a53ded67d593b000b9cab476c97cf5ab52d755776e90a5302dd2035ec","target":"graph","created_at":"2026-05-18T02:45:48Z","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 characterize all maximally entangling bipartite unitary operators, acting on systems $A,B$ of arbitrary finite dimensions $d_A\\le d_B$, when use of ancillary systems by both parties is allowed. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when $d_A=d_B$.","authors_text":"Scott M. Cohen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-19T23:19:19Z","title":"All maximally entangling unitary gates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4073","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":"sha256:5e88b78e4313a85f6739d97f6d40c5f03a203f8657a2b3b8af1a388692b0fee7","target":"record","created_at":"2026-05-18T02:45:48Z","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":"f2bc514a20ba21d47e425fd636f46208697886d2fdec1d1bc8d945ff2035f91a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-08-19T23:19:19Z","title_canon_sha256":"7e7c6bd06baf3579ef0651ee9f7449fa1e81b4b1f038bedcc68a88d71f209c7d"},"schema_version":"1.0","source":{"id":"1108.4073","kind":"arxiv","version":1}},"canonical_sha256":"105d7b1af32468e0141e4d6244881a568a3f9cb16bee36338e32837c28037f08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"105d7b1af32468e0141e4d6244881a568a3f9cb16bee36338e32837c28037f08","first_computed_at":"2026-05-18T02:45:48.917275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:48.917275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zYT4Pc8Fyuet7CdyHyMPRzsBbJvsdRC6UvjMUYD8fRKSWK9IqY62DhuoOzZ4IBX5LEGfQXL0WUkN7bh8USRBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:48.917771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e88b78e4313a85f6739d97f6d40c5f03a203f8657a2b3b8af1a388692b0fee7","sha256:19541d1a53ded67d593b000b9cab476c97cf5ab52d755776e90a5302dd2035ec"],"state_sha256":"15161adbbdd2534b51859d320916d72a5bab3eb014e048222748a3da42441c44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HrRAWJOVXKAfv6jAUzwdxY35jvScl2KrRt/Ri13wETtSqYQ6kzW2o4EsOLI+egDADS+5/Iimb7zrZCIyJ+xEBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T11:07:16.273167Z","bundle_sha256":"24923c2e0c0de72f2f7d5f358b223b14504a7ce984069dfc91f5d81dd5af7190"}}