{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MHV6YVIXRR5CGBS3VWRTGSFW7J","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":"defbddfd205155b084fa74b45127006d05c7042a3dee089a50c1a4bae1dea24b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-09-29T13:57:19Z","title_canon_sha256":"a58dcc8b4901a1504801a9d2eb581e46ea389d9486a7c98f854581ef19ae0637"},"schema_version":"1.0","source":{"id":"0909.5347","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5347","created_at":"2026-05-18T04:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5347v2","created_at":"2026-05-18T04:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5347","created_at":"2026-05-18T04:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"MHV6YVIXRR5C","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MHV6YVIXRR5CGBS3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MHV6YVIX","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:9f477e56f9d0c34f57dc5da87124f32070d5cfcf1cc2fb53b5013be1cd75ca5b","target":"graph","created_at":"2026-05-18T04:20:59Z","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 this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero--error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state.","authors_text":"D. Perez-Garcia, J. I. Cirac, M. M. Wolf, M. Sanz","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-09-29T13:57:19Z","title":"A quantum version of Wielandt's inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5347","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":"sha256:6ab54e50929b4b94777f32389a1528d0b3b3a8653051959d5ca54da1d82883e9","target":"record","created_at":"2026-05-18T04:20:59Z","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":"defbddfd205155b084fa74b45127006d05c7042a3dee089a50c1a4bae1dea24b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-09-29T13:57:19Z","title_canon_sha256":"a58dcc8b4901a1504801a9d2eb581e46ea389d9486a7c98f854581ef19ae0637"},"schema_version":"1.0","source":{"id":"0909.5347","kind":"arxiv","version":2}},"canonical_sha256":"61ebec55178c7a23065bada33348b6fa52c30558dc40391b479fcedcb42b5c76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ebec55178c7a23065bada33348b6fa52c30558dc40391b479fcedcb42b5c76","first_computed_at":"2026-05-18T04:20:59.304466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:59.304466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TCBrRv2nQm3yCKaJp+7Ukn1rVjf8n4WZhm1ybYc3txHFY2ymrlWdY6A6D9Endg5jCXJcLeE+8intA3y81UBbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:59.305162Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5347","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ab54e50929b4b94777f32389a1528d0b3b3a8653051959d5ca54da1d82883e9","sha256:9f477e56f9d0c34f57dc5da87124f32070d5cfcf1cc2fb53b5013be1cd75ca5b"],"state_sha256":"12c413494d80e1848f2ecc7345ae6e75289fe5a15517a6e92d5c26edcf2fc4a1"}