{"paper":{"title":"Tight Bounds for Quantum State Certification with Incoherent Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","cs.LG","math.IT"],"primary_cat":"quant-ph","authors_text":"Allen Liu, Brice Huang, Jerry Li, Sitan Chen","submitted_at":"2022-04-14T17:59:31Z","abstract_excerpt":"We consider the problem of quantum state certification, where we are given the description of a mixed state $\\sigma \\in \\mathbb{C}^{d \\times d}$, $n$ copies of a mixed state $\\rho \\in \\mathbb{C}^{d \\times d}$, and $\\varepsilon > 0$, and we are asked to determine whether $\\rho = \\sigma$ or whether $\\| \\rho - \\sigma \\|_1 > \\varepsilon$. When $\\sigma$ is the maximally mixed state $\\frac{1}{d} I_d$, this is known as mixedness testing. We focus on algorithms which use incoherent measurements, i.e. which only measure one copy of $\\rho$ at a time. Unlike those that use entangled, multi-copy measureme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07155","kind":"arxiv","version":2},"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/2204.07155/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"}