{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7AE7Q2ZWFDEDNE4ERPUMR6WYX7","short_pith_number":"pith:7AE7Q2ZW","canonical_record":{"source":{"id":"1008.1138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-06T09:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"1938144b452309d233dbc687b58650ee2b0433be8b07a7bfa571960b97538841","abstract_canon_sha256":"2827685523637a10dbed736173414c8cabb5d6cc867d65eb9a9cf2fbd10359e6"},"schema_version":"1.0"},"canonical_sha256":"f809f86b3628c83693848be8c8fad8bfd4617aed2c8dc67c744478024897afe1","source":{"kind":"arxiv","id":"1008.1138","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1138","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1138v1","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1138","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"7AE7Q2ZWFDED","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AE7Q2ZWFDEDNE4E","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AE7Q2ZW","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7AE7Q2ZWFDEDNE4ERPUMR6WYX7","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-06T09:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"1938144b452309d233dbc687b58650ee2b0433be8b07a7bfa571960b97538841","abstract_canon_sha256":"2827685523637a10dbed736173414c8cabb5d6cc867d65eb9a9cf2fbd10359e6"},"schema_version":"1.0"},"canonical_sha256":"f809f86b3628c83693848be8c8fad8bfd4617aed2c8dc67c744478024897afe1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:03.465676Z","signature_b64":"LjzWU01l7dqYp12Kl7aLVTWORDUPSCqwmSONnLDTb/fx32GwK7f5d2fGEkvrHMb9D3sNWhr77zEOigJICoRsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f809f86b3628c83693848be8c8fad8bfd4617aed2c8dc67c744478024897afe1","last_reissued_at":"2026-05-18T02:46:03.465175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:03.465175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1138","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":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsWcnRM81OOd+/XYfNxdGSsFnKB065KMOBuL0oT3EBvAkh5tPOiJ2zAShFFzMf7t3pA2Z5s4sJnqCoozSc7vCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:46:05.817767Z"},"content_sha256":"63445d5ce7e26e55967f47b7ce869951381dc45477438071d9fd0d6295b5816e","schema_version":"1.0","event_id":"sha256:63445d5ce7e26e55967f47b7ce869951381dc45477438071d9fd0d6295b5816e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7AE7Q2ZWFDEDNE4ERPUMR6WYX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure of Two-qubit Symmetric Informationally Complete POVMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Berthold-Georg Englert, Huangjun Zhu, Yong Siah Teo","submitted_at":"2010-08-06T09:04:06Z","abstract_excerpt":"In the four-dimensional Hilbert space, there exist 16 Heisenberg--Weyl (HW) covariant symmetric informationally complete positive operator valued measures (SIC~POVMs) consisting of 256 fiducial states on a single orbit of the Clifford group. We explore the structure of these SIC~POVMs by studying the symmetry transformations within a given SIC~POVM and among different SIC~POVMs. Furthermore, we find 16 additional SIC~POVMs by a regrouping of the 256 fiducial states, and show that they are unitarily equivalent to the original 16 SIC~POVMs by establishing an explicit unitary transformation. We t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1138","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":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lR/qdM3WAGBQbspI+PqJIcOOMviTXqyhSndUsf5l98rQmZQrpnpvmtEERCD4p4xzeE7YcYRlJd95oBRle+QNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:46:05.818113Z"},"content_sha256":"16d654a62fb19ccfd1dae3cc54a2348ee1384ba5b348add2cd13c93067680e30","schema_version":"1.0","event_id":"sha256:16d654a62fb19ccfd1dae3cc54a2348ee1384ba5b348add2cd13c93067680e30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/bundle.json","state_url":"https://pith.science/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/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":"2026-05-30T07:46:05Z","links":{"resolver":"https://pith.science/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7","bundle":"https://pith.science/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/bundle.json","state":"https://pith.science/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AE7Q2ZWFDEDNE4ERPUMR6WYX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7AE7Q2ZWFDEDNE4ERPUMR6WYX7","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":"2827685523637a10dbed736173414c8cabb5d6cc867d65eb9a9cf2fbd10359e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-06T09:04:06Z","title_canon_sha256":"1938144b452309d233dbc687b58650ee2b0433be8b07a7bfa571960b97538841"},"schema_version":"1.0","source":{"id":"1008.1138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1138","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1138v1","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1138","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"7AE7Q2ZWFDED","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AE7Q2ZWFDEDNE4E","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AE7Q2ZW","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:16d654a62fb19ccfd1dae3cc54a2348ee1384ba5b348add2cd13c93067680e30","target":"graph","created_at":"2026-05-18T02:46:03Z","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":"In the four-dimensional Hilbert space, there exist 16 Heisenberg--Weyl (HW) covariant symmetric informationally complete positive operator valued measures (SIC~POVMs) consisting of 256 fiducial states on a single orbit of the Clifford group. We explore the structure of these SIC~POVMs by studying the symmetry transformations within a given SIC~POVM and among different SIC~POVMs. Furthermore, we find 16 additional SIC~POVMs by a regrouping of the 256 fiducial states, and show that they are unitarily equivalent to the original 16 SIC~POVMs by establishing an explicit unitary transformation. We t","authors_text":"Berthold-Georg Englert, Huangjun Zhu, Yong Siah Teo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-06T09:04:06Z","title":"Structure of Two-qubit Symmetric Informationally Complete POVMs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1138","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":"sha256:63445d5ce7e26e55967f47b7ce869951381dc45477438071d9fd0d6295b5816e","target":"record","created_at":"2026-05-18T02:46:03Z","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":"2827685523637a10dbed736173414c8cabb5d6cc867d65eb9a9cf2fbd10359e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-06T09:04:06Z","title_canon_sha256":"1938144b452309d233dbc687b58650ee2b0433be8b07a7bfa571960b97538841"},"schema_version":"1.0","source":{"id":"1008.1138","kind":"arxiv","version":1}},"canonical_sha256":"f809f86b3628c83693848be8c8fad8bfd4617aed2c8dc67c744478024897afe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f809f86b3628c83693848be8c8fad8bfd4617aed2c8dc67c744478024897afe1","first_computed_at":"2026-05-18T02:46:03.465175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:03.465175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjzWU01l7dqYp12Kl7aLVTWORDUPSCqwmSONnLDTb/fx32GwK7f5d2fGEkvrHMb9D3sNWhr77zEOigJICoRsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:03.465676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63445d5ce7e26e55967f47b7ce869951381dc45477438071d9fd0d6295b5816e","sha256:16d654a62fb19ccfd1dae3cc54a2348ee1384ba5b348add2cd13c93067680e30"],"state_sha256":"b88c3092acbeee0e05caafccc9a132c3ffa95af43a9b8a950c07f60d68fe39bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oRx9wBLJhl7tGi/lzk5xL0EzrbJMQHPfPIAhQeDrCrUc2A6JPFs/QUnBqKjL027lkg8b6l0RNhdzV5jy55MjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:46:05.820241Z","bundle_sha256":"51f0f32e7733540b4aa371aaa568714e028051ac0e7ed72580d2954eed76a618"}}