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A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.<\/jats:p>","DOI":"10.22331\/q-2021-03-23-418","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T10:32:24Z","timestamp":1616495544000},"page":"418","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Device-independent certification of tensor products of quantum states using single-copy self-testing protocols"],"prefix":"10.22331","volume":"5","author":[{"given":"Ivan","family":"\u0160upi\u0107","sequence":"first","affiliation":[{"name":"D\u00e9partement de Physique Appliqu\u00e9e, Universit\u00e9 de Gen\u00e8ve, 1211 Gen\u00e8ve, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Cavalcanti","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Bowles","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Antonio Ac\u00edn, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani. 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