{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GH3Q6WAITGEMCZRTK3MSTKQRGJ","short_pith_number":"pith:GH3Q6WAI","canonical_record":{"source":{"id":"1109.2197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-10T06:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"3d3b281b51f65271a87dfdc4c4f0d4ab17ef9f43fd008692407dece336c0f930","abstract_canon_sha256":"12885854716acf84a9512f96d6616dbd650a2c2f0faf55ba6537162cc31b4dc8"},"schema_version":"1.0"},"canonical_sha256":"31f70f58089988c1663356d929aa11326f9f44f53d1c6c67ba91e734da71bc7d","source":{"kind":"arxiv","id":"1109.2197","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2197","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2197v2","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2197","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"pith_short_12","alias_value":"GH3Q6WAITGEM","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GH3Q6WAITGEMCZRT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GH3Q6WAI","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GH3Q6WAITGEMCZRTK3MSTKQRGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-10T06:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"3d3b281b51f65271a87dfdc4c4f0d4ab17ef9f43fd008692407dece336c0f930","abstract_canon_sha256":"12885854716acf84a9512f96d6616dbd650a2c2f0faf55ba6537162cc31b4dc8"},"schema_version":"1.0"},"canonical_sha256":"31f70f58089988c1663356d929aa11326f9f44f53d1c6c67ba91e734da71bc7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:36.787080Z","signature_b64":"QOklA09JawhZwZJ6GeExyqTcX+7w3SrLju0PeDAp+yp8GeVKLe1f2zALa6j9za/gz1VGh27QZEb4PZp2IV7SCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31f70f58089988c1663356d929aa11326f9f44f53d1c6c67ba91e734da71bc7d","last_reissued_at":"2026-05-18T02:00:36.786361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:36.786361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2197","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":"2026-05-18T02:00:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EpAbK685DB0JVVM0P+aEx7PClciXcmazukptUZFpg22WWBo7Htq+hJKeIY/Ao4k7YE+dJcMxCJ7/wixeRbOXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:24:32.272886Z"},"content_sha256":"bdb0452c4d9281708e375dc76097e7eb20cfc06ea59f784b2f70ff3b08b7f28a","schema_version":"1.0","event_id":"sha256:bdb0452c4d9281708e375dc76097e7eb20cfc06ea59f784b2f70ff3b08b7f28a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GH3Q6WAITGEMCZRTK3MSTKQRGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On unified-entropy characterization of quantum channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexey E. Rastegin","submitted_at":"2011-09-10T06:08:06Z","abstract_excerpt":"We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map $(q,s)$-entropy is naturally defined as the unified $(q,s)$-entropy of rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2197","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":"2026-05-18T02:00:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exLV0tK9B1BwBsS4+bUTMt9jOxTCdBtrT//32zfajinqYhMj28kDi4YQSdglI4m1LMkoZYDT92eV0Gp7fRakBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:24:32.273591Z"},"content_sha256":"e347eff188ad5f64996f77ad496e7ad1da5969182ad73f464bf34e326ffc2c8d","schema_version":"1.0","event_id":"sha256:e347eff188ad5f64996f77ad496e7ad1da5969182ad73f464bf34e326ffc2c8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/bundle.json","state_url":"https://pith.science/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/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":"2026-05-30T07:24:32Z","links":{"resolver":"https://pith.science/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ","bundle":"https://pith.science/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/bundle.json","state":"https://pith.science/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GH3Q6WAITGEMCZRTK3MSTKQRGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GH3Q6WAITGEMCZRTK3MSTKQRGJ","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":"12885854716acf84a9512f96d6616dbd650a2c2f0faf55ba6537162cc31b4dc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-10T06:08:06Z","title_canon_sha256":"3d3b281b51f65271a87dfdc4c4f0d4ab17ef9f43fd008692407dece336c0f930"},"schema_version":"1.0","source":{"id":"1109.2197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2197","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2197v2","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2197","created_at":"2026-05-18T02:00:36Z"},{"alias_kind":"pith_short_12","alias_value":"GH3Q6WAITGEM","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GH3Q6WAITGEMCZRT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GH3Q6WAI","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:e347eff188ad5f64996f77ad496e7ad1da5969182ad73f464bf34e326ffc2c8d","target":"graph","created_at":"2026-05-18T02:00:36Z","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 consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map $(q,s)$-entropy is naturally defined as the unified $(q,s)$-entropy of rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. T","authors_text":"Alexey E. Rastegin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-10T06:08:06Z","title":"On unified-entropy characterization of quantum channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2197","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:bdb0452c4d9281708e375dc76097e7eb20cfc06ea59f784b2f70ff3b08b7f28a","target":"record","created_at":"2026-05-18T02:00:36Z","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":"12885854716acf84a9512f96d6616dbd650a2c2f0faf55ba6537162cc31b4dc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-10T06:08:06Z","title_canon_sha256":"3d3b281b51f65271a87dfdc4c4f0d4ab17ef9f43fd008692407dece336c0f930"},"schema_version":"1.0","source":{"id":"1109.2197","kind":"arxiv","version":2}},"canonical_sha256":"31f70f58089988c1663356d929aa11326f9f44f53d1c6c67ba91e734da71bc7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31f70f58089988c1663356d929aa11326f9f44f53d1c6c67ba91e734da71bc7d","first_computed_at":"2026-05-18T02:00:36.786361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:36.786361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOklA09JawhZwZJ6GeExyqTcX+7w3SrLju0PeDAp+yp8GeVKLe1f2zALa6j9za/gz1VGh27QZEb4PZp2IV7SCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:36.787080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb0452c4d9281708e375dc76097e7eb20cfc06ea59f784b2f70ff3b08b7f28a","sha256:e347eff188ad5f64996f77ad496e7ad1da5969182ad73f464bf34e326ffc2c8d"],"state_sha256":"006934c0a80152cf5ecea640558781e0fa6873b785fa1fb3bd6ddf35158c0998"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgNW7C5XpRpyK3E2s6Qf5JwRwfko0RaDJk7ituX1/pWMJcp0psQLpQrSfAjmq0Ul/vptheHHs7VZgXVh5rx8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:24:32.276987Z","bundle_sha256":"5b35d01f0e5002a14351784cf5c58cff359c4bdb23b26bc636fde48e885b3c17"}}