{"paper":{"title":"Mana in Haar-random states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Christopher David White, Justin H. Wilson","submitted_at":"2020-11-27T19:00:01Z","abstract_excerpt":"Mana is a measure of the amount of non-Clifford resources required to create a state; the mana of a mixed state on $\\ell$ qudits bounded by $\\le \\frac 1 2 (\\ell \\ln d - S_2)$; $S_2$ the state's second Renyi entropy. We compute the mana of Haar-random pure and mixed states and find that the mana is nearly logarithmic in Hilbert space dimension: that is, extensive in number of qudits and logarithmic in qudit dimension. In particular, the average mana of states with less-than-maximal entropy falls short of that maximum by $\\ln \\pi/2$. We then connect this result to recent work on near-Clifford ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13937","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/2011.13937/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"}