{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NOLQYDDE2SLFERD4OUDMEIBG4Y","short_pith_number":"pith:NOLQYDDE","canonical_record":{"source":{"id":"1612.03363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-11T01:51:11Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"cc1fefe0116184311b748e9d4c3fa89e683e3bec05044954fca81494b5fa911f","abstract_canon_sha256":"e1854799ecf7f02f6c34e450dddcdd8ed435b980755e94619371464b6afe4905"},"schema_version":"1.0"},"canonical_sha256":"6b970c0c64d49652447c7506c22026e60aca61171d55ceb33cfe673434c2d10c","source":{"kind":"arxiv","id":"1612.03363","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03363","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03363v2","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03363","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"NOLQYDDE2SLF","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NOLQYDDE2SLFERD4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NOLQYDDE","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NOLQYDDE2SLFERD4OUDMEIBG4Y","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-11T01:51:11Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"cc1fefe0116184311b748e9d4c3fa89e683e3bec05044954fca81494b5fa911f","abstract_canon_sha256":"e1854799ecf7f02f6c34e450dddcdd8ed435b980755e94619371464b6afe4905"},"schema_version":"1.0"},"canonical_sha256":"6b970c0c64d49652447c7506c22026e60aca61171d55ceb33cfe673434c2d10c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:01.599358Z","signature_b64":"mFHdpoJndZwf/n+w7eiR2FtM4dcb1IEg+1fRodsK6tyFVlO1R+RNnwEfhauvJyyPsHuH3AqGh3/g8ddhnTTbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b970c0c64d49652447c7506c22026e60aca61171d55ceb33cfe673434c2d10c","last_reissued_at":"2026-05-18T00:26:01.598717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:01.598717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03363","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJgOQzATY/JVpc8tBvYmJhZ0aWL4XXbHXgOPppKAXUACENgF5dNlF1vHIESQzhv2gXO77COTWHhYSbxbpFAfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:31:28.179985Z"},"content_sha256":"10126eb365d24a61925a3a42a892c3d2f2da72db92310be8996297d44e650099","schema_version":"1.0","event_id":"sha256:10126eb365d24a61925a3a42a892c3d2f2da72db92310be8996297d44e650099"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NOLQYDDE2SLFERD4OUDMEIBG4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"primary_cat":"quant-ph","authors_text":"Anna Szczepanek, Wojciech S{\\l}omczy\\'nski","submitted_at":"2016-12-11T01:51:11Z","abstract_excerpt":"We introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies. They quantify the randomness of the successive quantum measurement results in the case where the evolution of the system between each two consecutive measurements is described by a given unitary operator. We study the class of chaotic unitaries, i.e., the ones of maximal entropy or, equivalently, such that they can be represented by suitably rescaled complex Hadamard matrices in some orthonormal bases. We provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03363","kind":"arxiv","version":2},"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":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncvKlUdvHG8wNl0tdM+VCJnCGWWbkruNBFqtNgQOIk8ieUEwmXsPVuGXRAwXZTYoFitnieExz9gBKj71WTalCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:31:28.180347Z"},"content_sha256":"5e7f367b9ecfe8abb344039bff2cf77de9e22a451987d6e96e8365fa1576c0da","schema_version":"1.0","event_id":"sha256:5e7f367b9ecfe8abb344039bff2cf77de9e22a451987d6e96e8365fa1576c0da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/bundle.json","state_url":"https://pith.science/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/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":"2026-06-25T05:31:28Z","links":{"resolver":"https://pith.science/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y","bundle":"https://pith.science/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/bundle.json","state":"https://pith.science/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOLQYDDE2SLFERD4OUDMEIBG4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NOLQYDDE2SLFERD4OUDMEIBG4Y","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":"e1854799ecf7f02f6c34e450dddcdd8ed435b980755e94619371464b6afe4905","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-11T01:51:11Z","title_canon_sha256":"cc1fefe0116184311b748e9d4c3fa89e683e3bec05044954fca81494b5fa911f"},"schema_version":"1.0","source":{"id":"1612.03363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03363","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03363v2","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03363","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"NOLQYDDE2SLF","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NOLQYDDE2SLFERD4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NOLQYDDE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:5e7f367b9ecfe8abb344039bff2cf77de9e22a451987d6e96e8365fa1576c0da","target":"graph","created_at":"2026-05-18T00:26:01Z","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 introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies. They quantify the randomness of the successive quantum measurement results in the case where the evolution of the system between each two consecutive measurements is described by a given unitary operator. We study the class of chaotic unitaries, i.e., the ones of maximal entropy or, equivalently, such that they can be represented by suitably rescaled complex Hadamard matrices in some orthonormal bases. We provide","authors_text":"Anna Szczepanek, Wojciech S{\\l}omczy\\'nski","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-11T01:51:11Z","title":"Quantum dynamical entropy, chaotic unitaries and complex Hadamard matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03363","kind":"arxiv","version":2},"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":"sha256:10126eb365d24a61925a3a42a892c3d2f2da72db92310be8996297d44e650099","target":"record","created_at":"2026-05-18T00:26:01Z","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":"e1854799ecf7f02f6c34e450dddcdd8ed435b980755e94619371464b6afe4905","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-11T01:51:11Z","title_canon_sha256":"cc1fefe0116184311b748e9d4c3fa89e683e3bec05044954fca81494b5fa911f"},"schema_version":"1.0","source":{"id":"1612.03363","kind":"arxiv","version":2}},"canonical_sha256":"6b970c0c64d49652447c7506c22026e60aca61171d55ceb33cfe673434c2d10c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b970c0c64d49652447c7506c22026e60aca61171d55ceb33cfe673434c2d10c","first_computed_at":"2026-05-18T00:26:01.598717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:01.598717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mFHdpoJndZwf/n+w7eiR2FtM4dcb1IEg+1fRodsK6tyFVlO1R+RNnwEfhauvJyyPsHuH3AqGh3/g8ddhnTTbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:01.599358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10126eb365d24a61925a3a42a892c3d2f2da72db92310be8996297d44e650099","sha256:5e7f367b9ecfe8abb344039bff2cf77de9e22a451987d6e96e8365fa1576c0da"],"state_sha256":"284c4d2d7acb119511369ddd2ca060462060417a5b3641b0156273dd1a7721e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jesrXUE9FNcY/V/fHxwAJC+owq4uBpScQDv8x0WwRN00/nRNFMe78Jkdiyp6anH+OFvbh9/qHgqYqAFwreG7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:31:28.182347Z","bundle_sha256":"fe48367c4f4560489c38e879457649228d01f8cc48c1b48a2e126804b1fd2133"}}