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In the simplest scenario, these guarantees are derived from the CHSH score, which is a simple linear combination of four correlation functions. We here derive a security proof from a generalisation of the CHSH score, which effectively takes into account the individual values of two correlation functions. We show that this additional information, which is anyway available in practice, allows one to get higher key rates than with the CHSH score. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.<\/jats:p>","DOI":"10.22331\/q-2021-04-26-444","type":"journal-article","created":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T14:57:42Z","timestamp":1619449062000},"page":"444","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":45,"title":["Device-independent quantum key distribution from generalized CHSH inequalities"],"prefix":"10.22331","volume":"5","author":[{"given":"Pavel","family":"Sekatski","sequence":"first","affiliation":[{"name":"Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Daniel","family":"Bancal","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, Chemin de Pinchat 22, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xavier","family":"Valcarce","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CEA, CNRS, Institut de physique th\u00e9orique, 91191, Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ernest Y.-Z.","family":"Tan","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, 8093 Z\u00fcrich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renato","family":"Renner","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, 8093 Z\u00fcrich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Sangouard","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland"},{"name":"Universit\u00e9 Paris-Saclay, CEA, CNRS, Institut de physique th\u00e9orique, 91191, Gif-sur-Yvette, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2021,4,26]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Artur K. 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