{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5OLOS7YWYF4SSCDFBF4DGENA3C","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":"5015ec4a7ca6deaec0cfe2e885e675f6d444b30fcf0364074690c4e10637f0b4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-07-17T19:36:28Z","title_canon_sha256":"0101e1152f1603b7b8445ab13fbcd19f09aea5482578c238d47518ebe303eb1d"},"schema_version":"1.0","source":{"id":"1907.07733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07733","created_at":"2026-07-05T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07733v2","created_at":"2026-07-05T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07733","created_at":"2026-07-05T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"5OLOS7YWYF4S","created_at":"2026-07-05T01:15:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OLOS7YWYF4SSCDF","created_at":"2026-07-05T01:15:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OLOS7YW","created_at":"2026-07-05T01:15:05Z"}],"graph_snapshots":[{"event_id":"sha256:ba03a4153ef80dceddc1d7328d69a09334fa86cb7df0b6e7f4cac3086d60b6aa","target":"graph","created_at":"2026-07-05T01:15:05Z","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/1907.07733/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length $n$ of all QMDS codes with local dimension $D$ and distance $d \\geq 3$ is bounded by $n \\leq D^2 + d - 2$. We obtain their weight distribution and present additional bounds that arise from Rains' shadow inequalities. Our main result can be seen as a generalization of bounds that are known for the two special cases of stabilizer QMDS codes and absolutely maximally entangled states, and confirms the quantum MDS conjecture in the special case of distance-three codes. As the existence of Q","authors_text":"Felix Huber, Markus Grassl","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-07-17T19:36:28Z","title":"Quantum Codes of Maximal Distance and Highly Entangled Subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07733","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:ed5cc1aea4b4814774fba5b236aab1b4102b86b7c739fdce2202eab9c26adc46","target":"record","created_at":"2026-07-05T01:15:05Z","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":"5015ec4a7ca6deaec0cfe2e885e675f6d444b30fcf0364074690c4e10637f0b4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2019-07-17T19:36:28Z","title_canon_sha256":"0101e1152f1603b7b8445ab13fbcd19f09aea5482578c238d47518ebe303eb1d"},"schema_version":"1.0","source":{"id":"1907.07733","kind":"arxiv","version":2}},"canonical_sha256":"eb96e97f16c17929086509783311a0d8a9717e930738989c442c501fb23e5626","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb96e97f16c17929086509783311a0d8a9717e930738989c442c501fb23e5626","first_computed_at":"2026-07-05T01:15:05.869918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:05.869918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mU0aQMizYtycsFNBsYb5c80gw4TRKM8+aZoxRBGNaX0E4kUj8WMQcZJ500Y8eJsgbx/VzuBfb4NfhGyh9fIDAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:05.870452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed5cc1aea4b4814774fba5b236aab1b4102b86b7c739fdce2202eab9c26adc46","sha256:ba03a4153ef80dceddc1d7328d69a09334fa86cb7df0b6e7f4cac3086d60b6aa"],"state_sha256":"c74fd7d0c79ab37745dd579e6adca47e7c6595a98945cdac94c3faea6119aebb"}