{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:A5DJ7OBRNBDSC44UBAI7QGSSQB","short_pith_number":"pith:A5DJ7OBR","canonical_record":{"source":{"id":"1209.2748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-12T22:50:32Z","cross_cats_sorted":[],"title_canon_sha256":"447719c9693808f29938a7da75ceaf2cf405f41bea477e8cf59f6273034a0bf4","abstract_canon_sha256":"c9c75803358ede971462489df55eb6a2b758f526acd5a5fc3c55cfc7ecdccb3f"},"schema_version":"1.0"},"canonical_sha256":"07469fb83168472173940811f81a52806ea1225d9afa2c730fedee527eb70ff8","source":{"kind":"arxiv","id":"1209.2748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2748","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2748v1","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2748","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"A5DJ7OBRNBDS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A5DJ7OBRNBDSC44U","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A5DJ7OBR","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:A5DJ7OBRNBDSC44UBAI7QGSSQB","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-12T22:50:32Z","cross_cats_sorted":[],"title_canon_sha256":"447719c9693808f29938a7da75ceaf2cf405f41bea477e8cf59f6273034a0bf4","abstract_canon_sha256":"c9c75803358ede971462489df55eb6a2b758f526acd5a5fc3c55cfc7ecdccb3f"},"schema_version":"1.0"},"canonical_sha256":"07469fb83168472173940811f81a52806ea1225d9afa2c730fedee527eb70ff8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:41.083258Z","signature_b64":"m4W5pyoQRRhfHKInypionM6AxFfYubysuOiDyMdeMeuiy4EwuX01rceasHYCHSFr09ogqgFQqjHsgm+SCeSGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07469fb83168472173940811f81a52806ea1225d9afa2c730fedee527eb70ff8","last_reissued_at":"2026-05-18T03:45:41.082549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:41.082549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2748","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FU4kENzd8rFE5vUMFHNOGi2s2QnoF8cLwXL7UnUmGjd+9Lsd+YV41NXVIoF0L5OzfAY0ENh30qOJK4YgwLIDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:11:10.207047Z"},"content_sha256":"596e2bb179c5fc76e44727aa3f9996b3c30bb92e36c4f29bcd25906c60b8ef19","schema_version":"1.0","event_id":"sha256:596e2bb179c5fc76e44727aa3f9996b3c30bb92e36c4f29bcd25906c60b8ef19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:A5DJ7OBRNBDSC44UBAI7QGSSQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pedagogical introduction to the entropy of entanglement for Gaussian states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tommaso F. Demarie","submitted_at":"2012-09-12T22:50:32Z","abstract_excerpt":"The most useful measure of a bipartite entanglement is the von Neumann entropy of either of the reduced density matrices. For a particular class of continuous-variable states, the Gaussian states, the entropy of entanglement can be expressed rather elegantly in terms of the symplectic eigenvalues, elements that characterize a Gaussian state and depend on the correlations of the canonical variables. We give a pedagogical step-by-step derivation of this result and provide some insights that can be useful in practical calculations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2748","kind":"arxiv","version":1},"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":"2026-05-18T03:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtafFRxjsk9zR4C3zndPDNu2VTHUQS5FENNDYdqdvSl2LBlzQsQbHdd6eAi38oqa+jwAkTme5CU8nWQfNZvpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:11:10.207457Z"},"content_sha256":"eb5b0337165389d44b79e4ed3f2155bc217b2ba033fd87449ce92dc86d9d9584","schema_version":"1.0","event_id":"sha256:eb5b0337165389d44b79e4ed3f2155bc217b2ba033fd87449ce92dc86d9d9584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/bundle.json","state_url":"https://pith.science/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/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":"2026-05-26T22:11:10Z","links":{"resolver":"https://pith.science/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB","bundle":"https://pith.science/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/bundle.json","state":"https://pith.science/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5DJ7OBRNBDSC44UBAI7QGSSQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A5DJ7OBRNBDSC44UBAI7QGSSQB","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":"c9c75803358ede971462489df55eb6a2b758f526acd5a5fc3c55cfc7ecdccb3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-12T22:50:32Z","title_canon_sha256":"447719c9693808f29938a7da75ceaf2cf405f41bea477e8cf59f6273034a0bf4"},"schema_version":"1.0","source":{"id":"1209.2748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2748","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2748v1","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2748","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"A5DJ7OBRNBDS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A5DJ7OBRNBDSC44U","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A5DJ7OBR","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:eb5b0337165389d44b79e4ed3f2155bc217b2ba033fd87449ce92dc86d9d9584","target":"graph","created_at":"2026-05-18T03:45:41Z","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":"The most useful measure of a bipartite entanglement is the von Neumann entropy of either of the reduced density matrices. For a particular class of continuous-variable states, the Gaussian states, the entropy of entanglement can be expressed rather elegantly in terms of the symplectic eigenvalues, elements that characterize a Gaussian state and depend on the correlations of the canonical variables. We give a pedagogical step-by-step derivation of this result and provide some insights that can be useful in practical calculations.","authors_text":"Tommaso F. Demarie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-12T22:50:32Z","title":"Pedagogical introduction to the entropy of entanglement for Gaussian states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2748","kind":"arxiv","version":1},"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":"sha256:596e2bb179c5fc76e44727aa3f9996b3c30bb92e36c4f29bcd25906c60b8ef19","target":"record","created_at":"2026-05-18T03:45:41Z","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":"c9c75803358ede971462489df55eb6a2b758f526acd5a5fc3c55cfc7ecdccb3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-12T22:50:32Z","title_canon_sha256":"447719c9693808f29938a7da75ceaf2cf405f41bea477e8cf59f6273034a0bf4"},"schema_version":"1.0","source":{"id":"1209.2748","kind":"arxiv","version":1}},"canonical_sha256":"07469fb83168472173940811f81a52806ea1225d9afa2c730fedee527eb70ff8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07469fb83168472173940811f81a52806ea1225d9afa2c730fedee527eb70ff8","first_computed_at":"2026-05-18T03:45:41.082549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:41.082549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m4W5pyoQRRhfHKInypionM6AxFfYubysuOiDyMdeMeuiy4EwuX01rceasHYCHSFr09ogqgFQqjHsgm+SCeSGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:41.083258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:596e2bb179c5fc76e44727aa3f9996b3c30bb92e36c4f29bcd25906c60b8ef19","sha256:eb5b0337165389d44b79e4ed3f2155bc217b2ba033fd87449ce92dc86d9d9584"],"state_sha256":"1303cdf2691310d5e72bd046988d6b5440d368818d5922ffe1a44801b18cc62e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o90uR8ErtvN/rDrDQ+z2SNixjyI483aN4yvKea+nMwDP87uxQlzlmHiVsOaMdCKfrOAghrgJzZT+awpo+z3KAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:11:10.210151Z","bundle_sha256":"01fa654dd7ef85062e317c6501971b33022fcfaed96c8a64ca368cdae480be10"}}