{"paper":{"title":"Certainty relations, mutual entanglement and non-displacable manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Karol \\.Zyczkowski, Krzysztof Chabuda, {\\L}ukasz Rudnicki, Miko{\\l}aj Paraniak, Zbigniew Pucha{\\l}a","submitted_at":"2015-06-25T11:39:27Z","abstract_excerpt":"We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size $N$ in $L$ orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate universal certainty relations. For $L=2$ the maximal average entropy saturates at $\\log N$ as there exists a mutually coherent state, but certainty relations are shown to be nontrivial for $L \\ge 3$ measurements. In the case of a prime power dimension, $N=p^k$, and the number of measurements $L=N+1$, the upper bound for the average entropy becomes minimal for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07709","kind":"arxiv","version":3},"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"}