{"paper":{"title":"Efficient quantum tomography II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"John Wright, Ryan O'Donnell","submitted_at":"2016-11-30T21:19:44Z","abstract_excerpt":"Following [OW16], we continue our analysis of: (1) \"Quantum tomography\", i.e., learning a quantum state, i.e., the quantum generalization of learning a discrete probability distribution; (2) The distribution of Young diagrams output by the RSK algorithm on random words. Regarding (2), we introduce two powerful new tools: (i) A precise upper bound on the expected length of the longest union of $k$ disjoint increasing subsequences in a random length-$n$ word with letter distribution $\\alpha_1 \\geq \\alpha_2 \\geq \\cdots \\geq \\alpha_d$; (ii) A new majorization property of the RSK algorithm that all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00034","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":""},"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"}