{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TWKMTU7FM2GFMDJXOJ65GVGCJZ","short_pith_number":"pith:TWKMTU7F","canonical_record":{"source":{"id":"1302.4525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T06:22:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"139cf3e499af06bd1de3a085d25bffbbb8db42297db216c6735f21f905562b14","abstract_canon_sha256":"49f1a60e7b2910887689869f4ed74a6d515d8b700255615e228ef52fd7156e68"},"schema_version":"1.0"},"canonical_sha256":"9d94c9d3e5668c560d37727dd354c24e73e368aa5eefba8664ba5d645a682b3b","source":{"kind":"arxiv","id":"1302.4525","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4525","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4525v2","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4525","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"TWKMTU7FM2GF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TWKMTU7FM2GFMDJX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TWKMTU7F","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TWKMTU7FM2GFMDJXOJ65GVGCJZ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T06:22:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"139cf3e499af06bd1de3a085d25bffbbb8db42297db216c6735f21f905562b14","abstract_canon_sha256":"49f1a60e7b2910887689869f4ed74a6d515d8b700255615e228ef52fd7156e68"},"schema_version":"1.0"},"canonical_sha256":"9d94c9d3e5668c560d37727dd354c24e73e368aa5eefba8664ba5d645a682b3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:56.779256Z","signature_b64":"R4nk3986TPIL96viFkKS6VqnAu4BRCpwDJF/YrfWhW0Oukb28YzX1x1dl2pA7bMFrTT4s6GESGqrCpAm6Xr2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d94c9d3e5668c560d37727dd354c24e73e368aa5eefba8664ba5d645a682b3b","last_reissued_at":"2026-05-18T03:17:56.778529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:56.778529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4525","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":"2026-05-18T03:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTb04EnPf1P3+sncYxc0rUFEWE71vYT9WGzyGRWrfirenJ5RbopXer7U19qtvI8zAzx1BSe0SCRJzpPxWN+VAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:45:12.619142Z"},"content_sha256":"ea331c5e36f45bf1bf790a9c35b8e48e5dbc4ad1510a0c0c024953cf7ed4ae37","schema_version":"1.0","event_id":"sha256:ea331c5e36f45bf1bf790a9c35b8e48e5dbc4ad1510a0c0c024953cf7ed4ae37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TWKMTU7FM2GFMDJXOJ65GVGCJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified-entropy trade-off relations for a single quantum channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alexey E. Rastegin","submitted_at":"2013-02-19T06:22:08Z","abstract_excerpt":"Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\\l}kowski-Choi representation, the given quantum channel is described by the so-called dynamical matrix. Entropies of the rescaled dynamical matrix known as map entropies describe a degree of introduced decoherence. Within the so-called natural representation, the quantum channel is formally posed by another matrix obtained as reshuffling of the dynamical matrix. The corresponding entrop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4525","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":"2026-05-18T03:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXHH7igJIJVuvX2dwTdORR4Fbj0VzEKFi1HR9u7gL6VMrWhjeDkHrmXhyP3Cpsy+OnREPDJARF/OpCMH/sIZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:45:12.619598Z"},"content_sha256":"3bbc86a8ed8ab0c716feb0552d318a1f59e1b256442c8391de92cd5c497dc7d5","schema_version":"1.0","event_id":"sha256:3bbc86a8ed8ab0c716feb0552d318a1f59e1b256442c8391de92cd5c497dc7d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/bundle.json","state_url":"https://pith.science/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/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":"2026-05-30T22:45:12Z","links":{"resolver":"https://pith.science/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ","bundle":"https://pith.science/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/bundle.json","state":"https://pith.science/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWKMTU7FM2GFMDJXOJ65GVGCJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TWKMTU7FM2GFMDJXOJ65GVGCJZ","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":"49f1a60e7b2910887689869f4ed74a6d515d8b700255615e228ef52fd7156e68","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T06:22:08Z","title_canon_sha256":"139cf3e499af06bd1de3a085d25bffbbb8db42297db216c6735f21f905562b14"},"schema_version":"1.0","source":{"id":"1302.4525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4525","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4525v2","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4525","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"TWKMTU7FM2GF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TWKMTU7FM2GFMDJX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TWKMTU7F","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:3bbc86a8ed8ab0c716feb0552d318a1f59e1b256442c8391de92cd5c497dc7d5","target":"graph","created_at":"2026-05-18T03:17:56Z","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":"Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\\l}kowski-Choi representation, the given quantum channel is described by the so-called dynamical matrix. Entropies of the rescaled dynamical matrix known as map entropies describe a degree of introduced decoherence. Within the so-called natural representation, the quantum channel is formally posed by another matrix obtained as reshuffling of the dynamical matrix. The corresponding entrop","authors_text":"Alexey E. Rastegin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T06:22:08Z","title":"Unified-entropy trade-off relations for a single quantum channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4525","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:ea331c5e36f45bf1bf790a9c35b8e48e5dbc4ad1510a0c0c024953cf7ed4ae37","target":"record","created_at":"2026-05-18T03:17:56Z","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":"49f1a60e7b2910887689869f4ed74a6d515d8b700255615e228ef52fd7156e68","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T06:22:08Z","title_canon_sha256":"139cf3e499af06bd1de3a085d25bffbbb8db42297db216c6735f21f905562b14"},"schema_version":"1.0","source":{"id":"1302.4525","kind":"arxiv","version":2}},"canonical_sha256":"9d94c9d3e5668c560d37727dd354c24e73e368aa5eefba8664ba5d645a682b3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d94c9d3e5668c560d37727dd354c24e73e368aa5eefba8664ba5d645a682b3b","first_computed_at":"2026-05-18T03:17:56.778529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:56.778529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R4nk3986TPIL96viFkKS6VqnAu4BRCpwDJF/YrfWhW0Oukb28YzX1x1dl2pA7bMFrTT4s6GESGqrCpAm6Xr2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:56.779256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea331c5e36f45bf1bf790a9c35b8e48e5dbc4ad1510a0c0c024953cf7ed4ae37","sha256:3bbc86a8ed8ab0c716feb0552d318a1f59e1b256442c8391de92cd5c497dc7d5"],"state_sha256":"d496b76ce8fe3ccce08b2f3d853ef4a267ce4e3abf4c57f1c71a4befe050af0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fb2Z0eaxWvPiCHuyMaX6qF/sl4VJsuuZQoA6gb15S41ABgJu6HwdLz9eqISMPGMMu5ucANdLbf/tM/KzQoIJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:45:12.623330Z","bundle_sha256":"82ecbae6b6182c3396b03f0eacd7ed9f60d7bf4ee852d14471d40266272de3e8"}}