{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CS6W2YZ5CDXQYKOG2Q6A6IPUTT","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":"cfe9f1ca1204a45e5e7c601ba6e222fb9ec81da296647af0754d5a23f2939f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-01T00:31:35Z","title_canon_sha256":"cda078ad5da219789ac37f7b3c0c24f7a56a9dcf7b6433b808181346d4efe38b"},"schema_version":"1.0","source":{"id":"1803.02673","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02673","created_at":"2026-07-05T08:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02673v2","created_at":"2026-07-05T08:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02673","created_at":"2026-07-05T08:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"CS6W2YZ5CDXQ","created_at":"2026-07-05T08:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CS6W2YZ5CDXQYKOG","created_at":"2026-07-05T08:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CS6W2YZ5","created_at":"2026-07-05T08:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9bdbd6ca183de8cbad18983bab4cacdf8fcfed0ab774a43b7c1b17e2524e527d","target":"graph","created_at":"2026-07-05T08:33:12Z","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/1803.02673/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The earth mover's distance is a measure of the distance between two probabilistic measures. It plays a fundamental role in mathematics and computer science. The Kantorovich-Rubinstein theorem provides a formula for the earth mover's distance on the space of regular probability Borel measures on a compact metric space. In this paper, we investigate the quantum earth mover's distance. We show a no-go Kantorovich-Rubinstein theorem in the quantum setting. More precisely, we show that the trace distance between two quantum states can not be determined by their earth mover's distance. The technique","authors_text":"Li Zhou, Mingsheng Ying, Nengkun Yu, Shenggang Ying","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-01T00:31:35Z","title":"Quantum Earth mover's distance, No-go Quantum Kantorovich-Rubinstein theorem, and Quantum Marginal Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02673","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":"sha256:348849e572eb66c4bc402e67d72b3961fcc5382cfc3ae602af6f0c87cdd9e890","target":"record","created_at":"2026-07-05T08:33:12Z","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":"cfe9f1ca1204a45e5e7c601ba6e222fb9ec81da296647af0754d5a23f2939f67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-01T00:31:35Z","title_canon_sha256":"cda078ad5da219789ac37f7b3c0c24f7a56a9dcf7b6433b808181346d4efe38b"},"schema_version":"1.0","source":{"id":"1803.02673","kind":"arxiv","version":2}},"canonical_sha256":"14bd6d633d10ef0c29c6d43c0f21f49cdbed9465469c976e8b9255cd814cff61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14bd6d633d10ef0c29c6d43c0f21f49cdbed9465469c976e8b9255cd814cff61","first_computed_at":"2026-07-05T08:33:12.421641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:12.421641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yh27vyWHVZm87FAOuIdkPyIYPQ8uDBJiiKwERPYdH8NOcjal7/hxQWifeVe8isdxi1Ydz1vlAlq5guVMykvsAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:12.422147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02673","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:348849e572eb66c4bc402e67d72b3961fcc5382cfc3ae602af6f0c87cdd9e890","sha256:9bdbd6ca183de8cbad18983bab4cacdf8fcfed0ab774a43b7c1b17e2524e527d"],"state_sha256":"04b2de59bd8209c206ea7c101d56354dec2557d4430aad690f2cba21707d5284"}