{"paper":{"title":"Coherent states with minimum Gini uncertainty for finite quantum systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"A. Vourdas, C. Lei","submitted_at":"2022-12-24T15:34:42Z","abstract_excerpt":"Uncertainty relations $\\Delta(\\rho)\\ge \\eta_d$ in terms of the Gini index are studied. The `Gini uncertainty constant' $\\eta_d$ is estimated numerically and compared to an upper bound $\\tilde \\eta_d\\ge \\eta_d$. It is shown that for large $d$ we get $\\tilde \\eta_d\\approx \\eta_d$. States $\\ket{g}$ with minimum Gini uncertainty and displacement transformations are used to define coherent states $\\ket{\\alpha, \\beta}_g$ (where $\\alpha, \\beta \\in {\\mathbb Z}_d$) with minimum Gini uncertainty ($\\Delta[\\ket{\\alpha, \\beta}_g\\;_g\\bra{\\alpha, \\beta}]\\approx \\eta_d$). The $\\ket{\\alpha, \\beta}_g$ resolve t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12755","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/2212.12755/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"}