{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:J6I5SMYLCZSDPGEV3BDW2VRYJG","short_pith_number":"pith:J6I5SMYL","canonical_record":{"source":{"id":"1706.00440","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-01T18:00:35Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"title_canon_sha256":"ddd9959a7a32e4a1cda9125f9818136d482055b3177ed0606b03e9922d0f35f9","abstract_canon_sha256":"86adc501cf74a643509afa8f38f862ebb649945d74392306aca85ae078087832"},"schema_version":"1.0"},"canonical_sha256":"4f91d9330b1664379895d8476d563849a21926237da8a6f2ce63cc68a60059c7","source":{"kind":"arxiv","id":"1706.00440","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00440","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00440v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00440","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"J6I5SMYLCZSD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J6I5SMYLCZSDPGEV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J6I5SMYL","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:J6I5SMYLCZSDPGEV3BDW2VRYJG","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00440","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-01T18:00:35Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"title_canon_sha256":"ddd9959a7a32e4a1cda9125f9818136d482055b3177ed0606b03e9922d0f35f9","abstract_canon_sha256":"86adc501cf74a643509afa8f38f862ebb649945d74392306aca85ae078087832"},"schema_version":"1.0"},"canonical_sha256":"4f91d9330b1664379895d8476d563849a21926237da8a6f2ce63cc68a60059c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:28.953223Z","signature_b64":"LEkwPM5UfUQUE5qXklvVY9OoailB4u1dUBMcgXhzaG8qoOmVc1l3jNdB7lDsmw3JGiNSCozQGxFKxWN0k1PGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f91d9330b1664379895d8476d563849a21926237da8a6f2ce63cc68a60059c7","last_reissued_at":"2026-05-18T00:14:28.952553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:28.952553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00440","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":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmXBW2pwUAtwbO9A8LJ0soXREBJ5HstMXN5H7N6JzxzueG3KD106cQ3AwT4Rm3+dWk/NBI7R8Lcr/xmaKibXCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:47:35.784237Z"},"content_sha256":"a78f57b10834d718d025a67b31a34c199ad4ee402a9a0f8e4aa8cb53b06f3ccb","schema_version":"1.0","event_id":"sha256:a78f57b10834d718d025a67b31a34c199ad4ee402a9a0f8e4aa8cb53b06f3ccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:J6I5SMYLCZSDPGEV3BDW2VRYJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The conditional Entropy Power Inequality for bosonic quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"primary_cat":"math-ph","authors_text":"Dario Trevisan, Giacomo De Palma","submitted_at":"2017-06-01T18:00:35Z","abstract_excerpt":"We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically ach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00440","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":"2026-05-18T00:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXk3CvW0tBKDmBxoe2+5GxAs4gM31SYtF2QaNpJqqaf4hGgsDYO2MsyE09hRG0M+HC9vV6HRainDYdy6wiHVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:47:35.784620Z"},"content_sha256":"17a27b60a6a04310d2a736ec858475d500bb89917ddb9a8bb90162287a3f07a8","schema_version":"1.0","event_id":"sha256:17a27b60a6a04310d2a736ec858475d500bb89917ddb9a8bb90162287a3f07a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/bundle.json","state_url":"https://pith.science/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/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":"2026-05-30T18:47:35Z","links":{"resolver":"https://pith.science/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG","bundle":"https://pith.science/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/bundle.json","state":"https://pith.science/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6I5SMYLCZSDPGEV3BDW2VRYJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:J6I5SMYLCZSDPGEV3BDW2VRYJG","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":"86adc501cf74a643509afa8f38f862ebb649945d74392306aca85ae078087832","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-01T18:00:35Z","title_canon_sha256":"ddd9959a7a32e4a1cda9125f9818136d482055b3177ed0606b03e9922d0f35f9"},"schema_version":"1.0","source":{"id":"1706.00440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00440","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00440v2","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00440","created_at":"2026-05-18T00:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"J6I5SMYLCZSD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J6I5SMYLCZSDPGEV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J6I5SMYL","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:17a27b60a6a04310d2a736ec858475d500bb89917ddb9a8bb90162287a3f07a8","target":"graph","created_at":"2026-05-18T00:14:28Z","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 prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically ach","authors_text":"Dario Trevisan, Giacomo De Palma","cross_cats":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-01T18:00:35Z","title":"The conditional Entropy Power Inequality for bosonic quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00440","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:a78f57b10834d718d025a67b31a34c199ad4ee402a9a0f8e4aa8cb53b06f3ccb","target":"record","created_at":"2026-05-18T00:14:28Z","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":"86adc501cf74a643509afa8f38f862ebb649945d74392306aca85ae078087832","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-01T18:00:35Z","title_canon_sha256":"ddd9959a7a32e4a1cda9125f9818136d482055b3177ed0606b03e9922d0f35f9"},"schema_version":"1.0","source":{"id":"1706.00440","kind":"arxiv","version":2}},"canonical_sha256":"4f91d9330b1664379895d8476d563849a21926237da8a6f2ce63cc68a60059c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f91d9330b1664379895d8476d563849a21926237da8a6f2ce63cc68a60059c7","first_computed_at":"2026-05-18T00:14:28.952553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:28.952553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LEkwPM5UfUQUE5qXklvVY9OoailB4u1dUBMcgXhzaG8qoOmVc1l3jNdB7lDsmw3JGiNSCozQGxFKxWN0k1PGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:28.953223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78f57b10834d718d025a67b31a34c199ad4ee402a9a0f8e4aa8cb53b06f3ccb","sha256:17a27b60a6a04310d2a736ec858475d500bb89917ddb9a8bb90162287a3f07a8"],"state_sha256":"7513d9e651ee9701939c21205bb9e3f5648b42ab87be38a1f6c46afe1d4ad371"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NerpMidYE2n1mwcGYp5571KNY7bcRjLqb0fUj8RLkq+OE+DBoipHC4r/MZOQ7e3BdrTj2uj8SoXqu0DKH697DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:47:35.787067Z","bundle_sha256":"cf17587a33f1b2ab41af9739caa426797beebfafa9125be6e5bc08651d539241"}}