{"paper":{"title":"From minimal informationally complete measurements to orthocentric simplices and back again","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anna Szymusiak, Piotr Bereza, Wojciech S\\l{}omczy\\'nski","submitted_at":"2026-08-01T18:25:05Z","abstract_excerpt":"The reconstruction of unknown quantum states via minimal informationally complete measurements (MICs) is a cornerstone of quantum tomography. Although the statistical properties of these measurements are well-understood, their geometric structure has remained elusive. In this work, we establish a correspondence between the class of minimal $s$-tight informationally complete measurements, encompassing, among others, tight IC and morphophoric measurements, and the classical geometry of orthocentric simplices. In particular, we prove a three-way equivalence: a MIC is $s$-tight if and only if its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00809","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/2608.00809/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"}