{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X5OHTG7G3HFXBPQH7LYQELFJZ2","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":"74fda8623754a59312ee85154b5c54aed7b680247f2b39837c8d1f3f7619cebc","cross_cats_sorted":["cs.IT","math.IT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-25T21:59:00Z","title_canon_sha256":"32222449a5deb961be890d2174e925d99c19ff91300e59d48e69f07f4af15b82"},"schema_version":"1.0","source":{"id":"1302.6262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6262","created_at":"2026-05-18T03:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6262v1","created_at":"2026-05-18T03:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6262","created_at":"2026-05-18T03:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"X5OHTG7G3HFX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X5OHTG7G3HFXBPQH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X5OHTG7G","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:51cb36660eb772e729613c84d0d40c8d6af6d8bfc16c2f264106c02b0a8b791c","target":"graph","created_at":"2026-05-18T03:32:30Z","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 investigate the action of the depolarising (qubit) channel on permutation invariant input states. More specifically, we raise the question on which invariant subspaces the output of the depolarising channel, given such special input, is supported. An answer is given for equidistributed states on isotypical subspaces, also called symmetric Werner states. Horns problem and two of the corresponding inequalities are invoked as a method of proof.","authors_text":"Janis Noetzel","cross_cats":["cs.IT","math.IT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-25T21:59:00Z","title":"The depolarising channel and Horns problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6262","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":"sha256:04ba775a2a0d6b761661a5a2820d6502542784f7d3e4ff21ad4203d49ced587a","target":"record","created_at":"2026-05-18T03:32:30Z","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":"74fda8623754a59312ee85154b5c54aed7b680247f2b39837c8d1f3f7619cebc","cross_cats_sorted":["cs.IT","math.IT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-25T21:59:00Z","title_canon_sha256":"32222449a5deb961be890d2174e925d99c19ff91300e59d48e69f07f4af15b82"},"schema_version":"1.0","source":{"id":"1302.6262","kind":"arxiv","version":1}},"canonical_sha256":"bf5c799be6d9cb70be07faf1022ca9ce81bab483d626444fcad0ce5ff4fbec22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf5c799be6d9cb70be07faf1022ca9ce81bab483d626444fcad0ce5ff4fbec22","first_computed_at":"2026-05-18T03:32:30.876080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:30.876080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JnC6RnIqUQheOVFQHwsoRGk6KIWnYKJS79QFUa2Tg9bnkE64RtjrZHge5DB5MQPohIHZmTvAtp7XJwlfWg7CDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:30.876648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04ba775a2a0d6b761661a5a2820d6502542784f7d3e4ff21ad4203d49ced587a","sha256:51cb36660eb772e729613c84d0d40c8d6af6d8bfc16c2f264106c02b0a8b791c"],"state_sha256":"733d1f96af9d0e9bd3775c921336734d3d42964904abe3f11d2b1caf97e78a9a"}