{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ABKAMLYAOSP6JOKD3J7PAQEZHC","short_pith_number":"pith:ABKAMLYA","canonical_record":{"source":{"id":"1112.1027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-05T19:11:53Z","cross_cats_sorted":[],"title_canon_sha256":"b98d64cd5c649cc110032d0ec8a6b6f91b0b3f083c76fda729232163bdc338a8","abstract_canon_sha256":"2217b88bb40be251c4164e8590269ea13b27673d5d894d0ec82c50992e7d9fb0"},"schema_version":"1.0"},"canonical_sha256":"0054062f00749fe4b943da7ef040993895d76cbc84f6fcb56e88ba33c83a162e","source":{"kind":"arxiv","id":"1112.1027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1027","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1027v1","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1027","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"ABKAMLYAOSP6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ABKAMLYAOSP6JOKD","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ABKAMLYA","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ABKAMLYAOSP6JOKD3J7PAQEZHC","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-05T19:11:53Z","cross_cats_sorted":[],"title_canon_sha256":"b98d64cd5c649cc110032d0ec8a6b6f91b0b3f083c76fda729232163bdc338a8","abstract_canon_sha256":"2217b88bb40be251c4164e8590269ea13b27673d5d894d0ec82c50992e7d9fb0"},"schema_version":"1.0"},"canonical_sha256":"0054062f00749fe4b943da7ef040993895d76cbc84f6fcb56e88ba33c83a162e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.213420Z","signature_b64":"HZeAcaoPmjTBIH8MVyRUqjkXvbX9WpcdoVnGxTrMSVb7GJjsf2M0fusksMlGiV7zGztQjgcn0OU6r8v08rQxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0054062f00749fe4b943da7ef040993895d76cbc84f6fcb56e88ba33c83a162e","last_reissued_at":"2026-05-18T03:59:49.212860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.212860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1027","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vzzbIvWCLT0U18zqGx5oM9b49sHHaaFlvHon6cIOEQlabQfqMTrKEZmUNOq5Hpmazm03K0HF4gLhwa1OrW0FBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T20:23:48.240957Z"},"content_sha256":"26ece92d861fed6d8d24e2e120bcfe2cf384b3f249bf0715a6564ec4258022dd","schema_version":"1.0","event_id":"sha256:26ece92d861fed6d8d24e2e120bcfe2cf384b3f249bf0715a6564ec4258022dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ABKAMLYAOSP6JOKD3J7PAQEZHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The power of random measurements: measuring Tr(\\rho^n) on single copies of \\rho","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. W. J. Beenakker, S. J. van Enk","submitted_at":"2011-12-05T19:11:53Z","abstract_excerpt":"While it is known that Tr(\\rho^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(\\rho^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct \\rho)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1027","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHFtUT3tAkEMNrzJy4Z+0Q+8U64XIN9U1W9CaJzeL2I0mKIU2ZWWEGsj2AUVPhSt1CZEGL0hYj5OOOTRRE1mBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T20:23:48.241631Z"},"content_sha256":"af11e88a45fd3001d3f76650690fe7de4d2ccd505490b5527eff1c48dfe7e768","schema_version":"1.0","event_id":"sha256:af11e88a45fd3001d3f76650690fe7de4d2ccd505490b5527eff1c48dfe7e768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/bundle.json","state_url":"https://pith.science/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/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":"2026-05-23T20:23:48Z","links":{"resolver":"https://pith.science/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC","bundle":"https://pith.science/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/bundle.json","state":"https://pith.science/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABKAMLYAOSP6JOKD3J7PAQEZHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ABKAMLYAOSP6JOKD3J7PAQEZHC","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":"2217b88bb40be251c4164e8590269ea13b27673d5d894d0ec82c50992e7d9fb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-05T19:11:53Z","title_canon_sha256":"b98d64cd5c649cc110032d0ec8a6b6f91b0b3f083c76fda729232163bdc338a8"},"schema_version":"1.0","source":{"id":"1112.1027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1027","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1027v1","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1027","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"ABKAMLYAOSP6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ABKAMLYAOSP6JOKD","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ABKAMLYA","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:af11e88a45fd3001d3f76650690fe7de4d2ccd505490b5527eff1c48dfe7e768","target":"graph","created_at":"2026-05-18T03:59:49Z","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":"While it is known that Tr(\\rho^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(\\rho^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct \\rho).","authors_text":"C. W. J. Beenakker, S. J. van Enk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-05T19:11:53Z","title":"The power of random measurements: measuring Tr(\\rho^n) on single copies of \\rho"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1027","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":"sha256:26ece92d861fed6d8d24e2e120bcfe2cf384b3f249bf0715a6564ec4258022dd","target":"record","created_at":"2026-05-18T03:59:49Z","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":"2217b88bb40be251c4164e8590269ea13b27673d5d894d0ec82c50992e7d9fb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-05T19:11:53Z","title_canon_sha256":"b98d64cd5c649cc110032d0ec8a6b6f91b0b3f083c76fda729232163bdc338a8"},"schema_version":"1.0","source":{"id":"1112.1027","kind":"arxiv","version":1}},"canonical_sha256":"0054062f00749fe4b943da7ef040993895d76cbc84f6fcb56e88ba33c83a162e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0054062f00749fe4b943da7ef040993895d76cbc84f6fcb56e88ba33c83a162e","first_computed_at":"2026-05-18T03:59:49.212860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.212860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZeAcaoPmjTBIH8MVyRUqjkXvbX9WpcdoVnGxTrMSVb7GJjsf2M0fusksMlGiV7zGztQjgcn0OU6r8v08rQxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.213420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26ece92d861fed6d8d24e2e120bcfe2cf384b3f249bf0715a6564ec4258022dd","sha256:af11e88a45fd3001d3f76650690fe7de4d2ccd505490b5527eff1c48dfe7e768"],"state_sha256":"6c07971e07eaaa4e463bbc6c694ecdc01f1955b12c7c80c6f8cea1523708f6e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jKrGHeIJfYpYsACsMvpracwtjFqG4K5xfpLj2y1CtmDlxHdDYZBdKlf8o9plWGiNhR5mm4kcQz1mOoD4cBUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T20:23:48.245377Z","bundle_sha256":"259fa162de26306fe9a89d6b22f8df6f62b80603fd7a8e5b5ff7928ac518b396"}}