{"paper":{"title":"No-Go Theorems for Quantum Transport Metrics from Fixed Cost Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Minbo Gao, Tianshi Yu, Zhengfeng Ji","submitted_at":"2026-07-30T15:24:50Z","abstract_excerpt":"Coupling-based quantum optimal transport generalizes classical optimal transport by representing transport plans as bipartite states with prescribed marginals and evaluating their cost as the expectation of a fixed Hermitian operator. Friedland et al. [Phys. Rev. Lett. 129, 110402 (2022)] conjectured that the square root of the optimal cost associated with the SWAP projector is a metric in every dimension and that this property persists for nearby quantum cost matrices. Miller [arXiv:2607.07764] disproved both conjectures by constructing explicit diagonal qutrit counterexamples. Building on hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28358","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28358/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}