{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VDCVMKE6PBIGOJHYHYPNLUNIOD","short_pith_number":"pith:VDCVMKE6","canonical_record":{"source":{"id":"1610.08870","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-27T16:27:09Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"14a34213602dcc23b8a11f537c455f6294a3328dba508e0057712f7176c3b48d","abstract_canon_sha256":"676e344b296ba10bfaa05b696830b57b1da481eeaaaaaef3d3099e46c6fc78ed"},"schema_version":"1.0"},"canonical_sha256":"a8c556289e78506724f83e1ed5d1a870db1f456bbe8d6279115dfef2c9df1be4","source":{"kind":"arxiv","id":"1610.08870","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08870","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08870v5","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08870","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"VDCVMKE6PBIG","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_16","alias_value":"VDCVMKE6PBIGOJHY","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_8","alias_value":"VDCVMKE6","created_at":"2026-07-05T03:17:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VDCVMKE6PBIGOJHYHYPNLUNIOD","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08870","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-27T16:27:09Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"14a34213602dcc23b8a11f537c455f6294a3328dba508e0057712f7176c3b48d","abstract_canon_sha256":"676e344b296ba10bfaa05b696830b57b1da481eeaaaaaef3d3099e46c6fc78ed"},"schema_version":"1.0"},"canonical_sha256":"a8c556289e78506724f83e1ed5d1a870db1f456bbe8d6279115dfef2c9df1be4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:17:11.004859Z","signature_b64":"+mygPSICQ9dR/2FumVu8Sm+5oHYlhLf6QFOEUTwIORkQRTELzA8SMSv+lLInjarOHjdvdMR/fQQiMkps6aU4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8c556289e78506724f83e1ed5d1a870db1f456bbe8d6279115dfef2c9df1be4","last_reissued_at":"2026-07-05T03:17:11.004430Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:17:11.004430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08870","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Zjzqy45zA/ukf+b2H7fD1mqBP6dXba8D4OgYDbvox1LQVys0jUme1Ya6WACkPCNUC44nIfQc9g50fTDFpxuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:21:03.466569Z"},"content_sha256":"a24b307ac69f1ad232880e7da02a5ff8d44f0e8549ce8feaf2729006eeda6ccb","schema_version":"1.0","event_id":"sha256:a24b307ac69f1ad232880e7da02a5ff8d44f0e8549ce8feaf2729006eeda6ccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VDCVMKE6PBIGOJHYHYPNLUNIOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy","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":"M.E. Shirokov","submitted_at":"2016-10-27T16:27:09Z","abstract_excerpt":"We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the case of a multi-mode quantum oscillator as an input system.\n  First we prove continuity bounds for the output conditional mutual information for a single channel and for $n$ copies of a channel.\n  Then we obtain estimates for variation of the output Holevo quantity with respect to simultaneous variations of a channel and of an input ensemble.\n  As a result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08870","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1610.08870/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FsnwDC5BIC9wTn48vJE5xUY8WwARS0xyLnIFN8GwDC9yPEfPlb7MtDakVL61alVgjOtMgWCWTKxsEGkALLKrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:21:03.467159Z"},"content_sha256":"60a65b5cdfc91ea89d1f17df035ec0863717f44c2cc5773a9a23561d46282ac3","schema_version":"1.0","event_id":"sha256:60a65b5cdfc91ea89d1f17df035ec0863717f44c2cc5773a9a23561d46282ac3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/bundle.json","state_url":"https://pith.science/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/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":"2026-08-16T01:21:03Z","links":{"resolver":"https://pith.science/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD","bundle":"https://pith.science/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/bundle.json","state":"https://pith.science/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDCVMKE6PBIGOJHYHYPNLUNIOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VDCVMKE6PBIGOJHYHYPNLUNIOD","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":"676e344b296ba10bfaa05b696830b57b1da481eeaaaaaef3d3099e46c6fc78ed","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":"2016-10-27T16:27:09Z","title_canon_sha256":"14a34213602dcc23b8a11f537c455f6294a3328dba508e0057712f7176c3b48d"},"schema_version":"1.0","source":{"id":"1610.08870","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08870","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08870v5","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08870","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"VDCVMKE6PBIG","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_16","alias_value":"VDCVMKE6PBIGOJHY","created_at":"2026-07-05T03:17:11Z"},{"alias_kind":"pith_short_8","alias_value":"VDCVMKE6","created_at":"2026-07-05T03:17:11Z"}],"graph_snapshots":[{"event_id":"sha256:60a65b5cdfc91ea89d1f17df035ec0863717f44c2cc5773a9a23561d46282ac3","target":"graph","created_at":"2026-07-05T03:17:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1610.08870/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the case of a multi-mode quantum oscillator as an input system.\n  First we prove continuity bounds for the output conditional mutual information for a single channel and for $n$ copies of a channel.\n  Then we obtain estimates for variation of the output Holevo quantity with respect to simultaneous variations of a channel and of an input ensemble.\n  As a result ","authors_text":"M.E. Shirokov","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":"2016-10-27T16:27:09Z","title":"Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08870","kind":"arxiv","version":5},"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:a24b307ac69f1ad232880e7da02a5ff8d44f0e8549ce8feaf2729006eeda6ccb","target":"record","created_at":"2026-07-05T03:17:11Z","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":"676e344b296ba10bfaa05b696830b57b1da481eeaaaaaef3d3099e46c6fc78ed","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":"2016-10-27T16:27:09Z","title_canon_sha256":"14a34213602dcc23b8a11f537c455f6294a3328dba508e0057712f7176c3b48d"},"schema_version":"1.0","source":{"id":"1610.08870","kind":"arxiv","version":5}},"canonical_sha256":"a8c556289e78506724f83e1ed5d1a870db1f456bbe8d6279115dfef2c9df1be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8c556289e78506724f83e1ed5d1a870db1f456bbe8d6279115dfef2c9df1be4","first_computed_at":"2026-07-05T03:17:11.004430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:17:11.004430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+mygPSICQ9dR/2FumVu8Sm+5oHYlhLf6QFOEUTwIORkQRTELzA8SMSv+lLInjarOHjdvdMR/fQQiMkps6aU4Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:17:11.004859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08870","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a24b307ac69f1ad232880e7da02a5ff8d44f0e8549ce8feaf2729006eeda6ccb","sha256:60a65b5cdfc91ea89d1f17df035ec0863717f44c2cc5773a9a23561d46282ac3"],"state_sha256":"de213fcdeec2bf3676355531cf497f7df15884470c595f3079eab6aa7e02687d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0tkLopxIhfgHCA6dNY/G2gsVqP23BGXeIoUKd9ObU66isKjDXqM38p5lggBA8COv2cU+wnJnlJr0YuPexKsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:21:03.471339Z","bundle_sha256":"41a2a0f8632f6ad8f2a63651bc9e3c0ab7a2af3c157099441227ff9fb8c0b59d"}}