{"paper":{"title":"Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alexey E. Rastegin","submitted_at":"2013-03-19T01:57:22Z","abstract_excerpt":"We formulate uncertainty relations for mutually unbiased bases and symmetric informationally complete measurements in terms of the R\\'{e}nyi and Tsallis entropies. For arbitrary number of mutually unbiased bases in a finite-dimensional Hilbert space, we give a family of Tsallis $\\alpha$-entropic bounds for $\\alpha\\in(0;2]$. Relations in a model of detection inefficiences are obtained. In terms of R\\'{e}nyi's entropies, lower bounds are given for $\\alpha\\in[2;\\infty)$. State-dependent and state-independent forms of such bounds are both given. Uncertainty relations in terms of the min-entropy ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4467","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}