{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2F5DOUTYBTQL2JRH7M2KFL3D72","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":"198df38b307208c5a1f8d845f7c19d1f1b29fa60b47eae6e9bbc475dd355bc7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-12T12:59:27Z","title_canon_sha256":"4a6885c3bd06ae1a7aa75ea667f5a0bb6987febb5bef5582d0ff5b3e6c689b13"},"schema_version":"1.0","source":{"id":"1306.2811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2811","created_at":"2026-05-18T03:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2811v1","created_at":"2026-05-18T03:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2811","created_at":"2026-05-18T03:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"2F5DOUTYBTQL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2F5DOUTYBTQL2JRH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2F5DOUTY","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:6601f966d7fbaf95f705746aee2f6d90c5ec05a89bf49b8515c0a1fbc0a1c936","target":"graph","created_at":"2026-05-18T03:21:09Z","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 derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit perfect entanglers. We find that this volume corresponds to more than 84% of the total invariant volume of the space of two-qubit gates. This same metric is also used to determine the effective target sizes that selected gates will present in any quantum-control procedure designed to implement them.","authors_text":"Jiri Vala, Maurice O'Connor, Paul Watts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-12T12:59:27Z","title":"Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2811","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:b7a4f879c6df7b04e4d757fd85b3bc6cf69f8df9fea754c75a4c5ca909c5e6c0","target":"record","created_at":"2026-05-18T03:21:09Z","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":"198df38b307208c5a1f8d845f7c19d1f1b29fa60b47eae6e9bbc475dd355bc7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-12T12:59:27Z","title_canon_sha256":"4a6885c3bd06ae1a7aa75ea667f5a0bb6987febb5bef5582d0ff5b3e6c689b13"},"schema_version":"1.0","source":{"id":"1306.2811","kind":"arxiv","version":1}},"canonical_sha256":"d17a3752780ce0bd2627fb34a2af63fe8139ff8469bd52ce956b2102db149633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d17a3752780ce0bd2627fb34a2af63fe8139ff8469bd52ce956b2102db149633","first_computed_at":"2026-05-18T03:21:09.372725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:09.372725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWcmKOWRgtoSeqd+mayOWCD5ELdTuR62nBFG/JWMshO0IHFfUk7Ej5ZkzKvqMCrvFYXgRynAc+MGDSaR7aUADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:09.373437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7a4f879c6df7b04e4d757fd85b3bc6cf69f8df9fea754c75a4c5ca909c5e6c0","sha256:6601f966d7fbaf95f705746aee2f6d90c5ec05a89bf49b8515c0a1fbc0a1c936"],"state_sha256":"d73ba0bdd6ab290e0ffcd80043c612ba77e3d8178442e2c3f955e0cd9afeff3b"}