{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3J6F6DMSODXK3CQ5CLTUAOWCHK","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":"3e9fdc2bc5937f70ab92d77b89902c28e2caef5dfac10a7d5aab292f8f39eb92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-10-08T14:58:08Z","title_canon_sha256":"ee1150e1e32ed0ed585af889e3c6f74c4d21812b1aa94bc3dc822ad9828daaf9"},"schema_version":"1.0","source":{"id":"2510.07100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.07100","created_at":"2026-06-10T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2510.07100v2","created_at":"2026-06-10T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.07100","created_at":"2026-06-10T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"3J6F6DMSODXK","created_at":"2026-06-10T01:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"3J6F6DMSODXK3CQ5","created_at":"2026-06-10T01:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"3J6F6DMS","created_at":"2026-06-10T01:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:72c476c647b9a2468186f07dcdea16cc434329934348dc3f7cdf9bd19dc4340e","target":"graph","created_at":"2026-06-10T01:09:44Z","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/2510.07100/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G\\times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch--Gordan transforms, which naturally extends to the $G$-covariant quantum comb. By using this circuit decomposition, we propose a parametrized quantum comb with group symmetry, and derive the optimal quantum comb which transforms an unknown unitary operation $U\\in \\mathrm{SU}(d)$ into its inverse $U^\\dagger$ or transpose $U^\\top$. From numerics, we find a determi","authors_text":"Dmitry Grinko, Maris Ozols, Mio Murao, Satoshi Yoshida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-10-08T14:58:08Z","title":"Sequential quantum processes with group symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.07100","kind":"arxiv","version":2},"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:dc8fa387216e1e79a252ecf5d089deb57987b612b6222063e7a0aa0f28b22e67","target":"record","created_at":"2026-06-10T01:09:44Z","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":"3e9fdc2bc5937f70ab92d77b89902c28e2caef5dfac10a7d5aab292f8f39eb92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-10-08T14:58:08Z","title_canon_sha256":"ee1150e1e32ed0ed585af889e3c6f74c4d21812b1aa94bc3dc822ad9828daaf9"},"schema_version":"1.0","source":{"id":"2510.07100","kind":"arxiv","version":2}},"canonical_sha256":"da7c5f0d9270eead8a1d12e7403ac23ab0517cf3da0b12031c1539168a06cc97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7c5f0d9270eead8a1d12e7403ac23ab0517cf3da0b12031c1539168a06cc97","first_computed_at":"2026-06-10T01:09:44.790399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:44.790399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWhPYF8symslGvHrKSL2n6qV0C19AlvjEWCuWaHv+51PYWZd2CvDsIwtfk5wjUGuOZxygUSHaF5kIpct0pqHAw==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:44.791440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.07100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc8fa387216e1e79a252ecf5d089deb57987b612b6222063e7a0aa0f28b22e67","sha256:72c476c647b9a2468186f07dcdea16cc434329934348dc3f7cdf9bd19dc4340e"],"state_sha256":"5d8d274c32b3235b8bdca65368a2c19b71d5ea5930cd1b8d9ad323a7561e82d1"}