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In efforts to relax the assumption of measurement independence, Hardy's non-locality tests have been proposed as ideal candidates. In this paper, we introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states, as well as certify up to 1<\/mml:mn><\/mml:math> bit of local randomness. We then use these tilted Hardy tests to obtain an improvement in the generation rate in the state-of-the-art randomness amplification protocols for Santha-Vazirani (SV) sources with arbitrarily limited measurement independence. Our result shows that device-independent randomness amplification is possible for arbitrarily biased SV sources and from almost separable states. Finally, we introduce a family of Hardy tests for maximally entangled states of local dimension 4<\/mml:mn>,<\/mml:mo>8<\/mml:mn><\/mml:math> as the potential candidates for DI randomness extraction to certify up to the maximum possible 2<\/mml:mn>log<\/mml:mi>&#x2061;<\/mml:mo>d<\/mml:mi><\/mml:math> bits of global randomness.<\/jats:p>","DOI":"10.22331\/q-2023-09-15-1114","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T11:09:09Z","timestamp":1694776149000},"page":"1114","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Tilted Hardy paradoxes for device-independent randomness extraction"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8720-5476","authenticated-orcid":false,"given":"Shuai","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1119-8721","authenticated-orcid":false,"given":"Ravishankar","family":"Ramanathan","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3233-1336","authenticated-orcid":false,"given":"Pawe\u0142","family":"Horodecki","sequence":"additional","affiliation":[{"name":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Wita Stwosza 63, 80-308 Gda\u0144sk, Poland"},{"name":"Faculty of Applied Physics and Mathematics, Gda\u0144sk University of Technology, Gabriela Narutowicza 11\/12, 80-233 Gda\u0144sk, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Albert Einstein, Boris Podolsky, and Nathan Rosen. ``Can quantum-mechanical description of physical reality be considered complete?'' 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