{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TM2D43ACFNXHZM5NBYY23CQ7ED","short_pith_number":"pith:TM2D43AC","canonical_record":{"source":{"id":"1006.1426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-08T01:13:49Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"695e80b3487604885dec14ad36cb5b554249d5e59f95d87e60bb92c8e77f170a","abstract_canon_sha256":"d14b05deb008a244a87dbcfcce4292226399858e4cdbe2f01eed101839c2544d"},"schema_version":"1.0"},"canonical_sha256":"9b343e6c022b6e7cb3ad0e31ad8a1f20c3c93b94d0c8e7a73a480138ec1eddfe","source":{"kind":"arxiv","id":"1006.1426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1426","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1426v1","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1426","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"TM2D43ACFNXH","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_16","alias_value":"TM2D43ACFNXHZM5N","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_8","alias_value":"TM2D43AC","created_at":"2026-07-04T17:30:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TM2D43ACFNXHZM5NBYY23CQ7ED","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-08T01:13:49Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"695e80b3487604885dec14ad36cb5b554249d5e59f95d87e60bb92c8e77f170a","abstract_canon_sha256":"d14b05deb008a244a87dbcfcce4292226399858e4cdbe2f01eed101839c2544d"},"schema_version":"1.0"},"canonical_sha256":"9b343e6c022b6e7cb3ad0e31ad8a1f20c3c93b94d0c8e7a73a480138ec1eddfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:30:14.270859Z","signature_b64":"C5yAii+BFvTEJBAjjJRvWx6qoNzs3mMnAp31gzg/AkgByjo/Pdo1xTwgMH8M/Scd6yOzgfjw4n3tu7u0me6MBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b343e6c022b6e7cb3ad0e31ad8a1f20c3c93b94d0c8e7a73a480138ec1eddfe","last_reissued_at":"2026-07-04T17:30:14.270455Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:30:14.270455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1426","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":"2026-07-04T17:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TgqqbtOHjic6dvMLvWDQVr+4hm4SqGXo/WmwYMVLrj/uskf2Hs78b6fUEZ907MWZJpvLrBHmpomKmug0oPrUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:20:42.659681Z"},"content_sha256":"8151a25bf00d0f5f43af7a68536a99ad4253ed8dc5816c34a8e19f6fa3007da8","schema_version":"1.0","event_id":"sha256:8151a25bf00d0f5f43af7a68536a99ad4253ed8dc5816c34a8e19f6fa3007da8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TM2D43ACFNXHZM5NBYY23CQ7ED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of delocalization power of global unitary operations in terms of LOCC one-piece relocalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Akihito Soeda, Mio Murao","submitted_at":"2010-06-08T01:13:49Z","abstract_excerpt":"We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied.  We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource.  We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation.   The delocalization power turns out to reveal different aspect of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1426","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1006.1426/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":"2026-07-04T17:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dL70YxYM9LRpVl7GOMq5V/WXig/WWWtWz2UEL2J7O15fk+pWU6bVpfm4jUGJG2ZTZluikMdDZ0RJ2Mpp0+TSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:20:42.660204Z"},"content_sha256":"96a134193445cec128d5226affa015d537de7175947aaae14737d15466b84a64","schema_version":"1.0","event_id":"sha256:96a134193445cec128d5226affa015d537de7175947aaae14737d15466b84a64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/bundle.json","state_url":"https://pith.science/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/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":"2026-08-03T23:20:42Z","links":{"resolver":"https://pith.science/pith/TM2D43ACFNXHZM5NBYY23CQ7ED","bundle":"https://pith.science/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/bundle.json","state":"https://pith.science/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM2D43ACFNXHZM5NBYY23CQ7ED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TM2D43ACFNXHZM5NBYY23CQ7ED","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":"d14b05deb008a244a87dbcfcce4292226399858e4cdbe2f01eed101839c2544d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-08T01:13:49Z","title_canon_sha256":"695e80b3487604885dec14ad36cb5b554249d5e59f95d87e60bb92c8e77f170a"},"schema_version":"1.0","source":{"id":"1006.1426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1426","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1426v1","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1426","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"TM2D43ACFNXH","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_16","alias_value":"TM2D43ACFNXHZM5N","created_at":"2026-07-04T17:30:14Z"},{"alias_kind":"pith_short_8","alias_value":"TM2D43AC","created_at":"2026-07-04T17:30:14Z"}],"graph_snapshots":[{"event_id":"sha256:96a134193445cec128d5226affa015d537de7175947aaae14737d15466b84a64","target":"graph","created_at":"2026-07-04T17:30:14Z","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/1006.1426/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied.  We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource.  We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation.   The delocalization power turns out to reveal different aspect of the","authors_text":"Akihito Soeda, Mio Murao","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-08T01:13:49Z","title":"Classification of delocalization power of global unitary operations in terms of LOCC one-piece relocalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1426","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":"sha256:8151a25bf00d0f5f43af7a68536a99ad4253ed8dc5816c34a8e19f6fa3007da8","target":"record","created_at":"2026-07-04T17:30:14Z","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":"d14b05deb008a244a87dbcfcce4292226399858e4cdbe2f01eed101839c2544d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-08T01:13:49Z","title_canon_sha256":"695e80b3487604885dec14ad36cb5b554249d5e59f95d87e60bb92c8e77f170a"},"schema_version":"1.0","source":{"id":"1006.1426","kind":"arxiv","version":1}},"canonical_sha256":"9b343e6c022b6e7cb3ad0e31ad8a1f20c3c93b94d0c8e7a73a480138ec1eddfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b343e6c022b6e7cb3ad0e31ad8a1f20c3c93b94d0c8e7a73a480138ec1eddfe","first_computed_at":"2026-07-04T17:30:14.270455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:30:14.270455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5yAii+BFvTEJBAjjJRvWx6qoNzs3mMnAp31gzg/AkgByjo/Pdo1xTwgMH8M/Scd6yOzgfjw4n3tu7u0me6MBw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:30:14.270859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8151a25bf00d0f5f43af7a68536a99ad4253ed8dc5816c34a8e19f6fa3007da8","sha256:96a134193445cec128d5226affa015d537de7175947aaae14737d15466b84a64"],"state_sha256":"fcf920d45f951afeec6b7f9d7d988c06a64ba14a076fe4cf8cb6681af8cc6e7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdj461jK/z7BH+DcBCFBue6mLKBJ1SO/41juBCNPIS2RhII/9L90jb3Z0SCGc1c54LV/EP4PltT4vn/WcU1DCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T23:20:42.663899Z","bundle_sha256":"a8c538fa015b41b4d51b7204df00dbbfc07048953f710ef8ac73444a1fb4c805"}}