{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z6SJ2A5BMEBHOUYYNIE3VXGG2C","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":"b9d3ef702910d3632be6742459a9af10e106d7defe8f38391bd2c6fe372ebb97","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-31T13:07:11Z","title_canon_sha256":"3d9b181baac5687e18812c2c1ce6292bc347c99d5c14c3ca4b0585310057e598"},"schema_version":"1.0","source":{"id":"1708.09696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09696","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09696v2","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09696","created_at":"2026-05-18T00:26:29Z"},{"alias_kind":"pith_short_12","alias_value":"Z6SJ2A5BMEBH","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z6SJ2A5BMEBHOUYY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z6SJ2A5B","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:0e12be1cc92b4211ff2e5b6c58c586550c550d85c91f3deea91b4cafa8554d05","target":"graph","created_at":"2026-05-18T00:26:29Z","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 we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. For synchronous correlations, we show a correspondence between the minimal entanglement dimension and the completely positive sem","authors_text":"David de Laat, Monique Laurent, Sander Gribling","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-31T13:07:11Z","title":"Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09696","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:d8acb983b7f4b7da78d398ae78ec16ef3c3acd55a3dabd7802e5ab28cea237b6","target":"record","created_at":"2026-05-18T00:26:29Z","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":"b9d3ef702910d3632be6742459a9af10e106d7defe8f38391bd2c6fe372ebb97","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-31T13:07:11Z","title_canon_sha256":"3d9b181baac5687e18812c2c1ce6292bc347c99d5c14c3ca4b0585310057e598"},"schema_version":"1.0","source":{"id":"1708.09696","kind":"arxiv","version":2}},"canonical_sha256":"cfa49d03a161027753186a09badcc6d0836ad5289ef5e099f890fb0f66d61b4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfa49d03a161027753186a09badcc6d0836ad5289ef5e099f890fb0f66d61b4a","first_computed_at":"2026-05-18T00:26:29.053082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:29.053082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zb1MJ6cup6Hqhjw+FI5mAKoPh743wf36zW0IVSxGwAS/9sjmL0w8O/TmnAM907Ftybe8LWheMintYo9XF8PdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:29.053638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8acb983b7f4b7da78d398ae78ec16ef3c3acd55a3dabd7802e5ab28cea237b6","sha256:0e12be1cc92b4211ff2e5b6c58c586550c550d85c91f3deea91b4cafa8554d05"],"state_sha256":"7e6d7248730d02748160657e2418ba1b855a68fcea843685fee397edd5942c94"}