There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity [OW15, OW16, HHJ+17, OW17, AISW19, BOW19]. Unfortunately, they require the use of entangled measurements across many copies of the underlying state and thus remain outside the realm of what is currently experimentally feasible. A natural question is whether one can match the copy complexity of such algorithms using only independent\u2014but possibly adaptively chosen\u2014measurements on individual copies.<\/p>\n
We answer this in the negative for arguably the most basic quantum testing problem: deciding whether a given d<\/em>-dimensional quantum state is equal to or \u01eb-far in trace distance from the maximally mixed state. While it is known how to achieve optimal O<\/em>(d<\/em>\/\u01eb2 ) copy complexity using entangled measurements, we show that with independent measurements, \u2126(d<\/em> 4\/3\/\u01eb2 ) is necessary, even if the measurements are chosen adaptively. This resolves a question posed in [Wri16]. To obtain this lower bound, we develop several new techniques, including a chain-rule style proof of Paninski\u2019s lower bound for classical uniformity testing, which may be of independent interest.<\/p>\n","protected":false},"excerpt":{"rendered":" There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity [OW15, OW16, HHJ+17, OW17, AISW19, BOW19]. Unfortunately, they require the use of entangled measurements across many copies of the underlying state and thus remain outside the realm of what is currently […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"FOCS 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