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The advent of DI-QKD closes several loopholes and side-channels that plague current QKD systems. While implementing DI-QKD protocols is technically challenging, there have been recent proof-of-principle demonstrations, resulting from the progress made in both theory and experiments. In this review, we will provide an introduction to DI-QKD, an overview of the related experiments performed, and the theory and techniques required to analyse its security. We conclude with an outlook on future DI-QKD research.<\/jats:p>","DOI":"10.22331\/q-2023-03-02-932","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T15:35:13Z","timestamp":1677771313000},"page":"932","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":59,"title":["Security of device-independent quantum key distribution protocols: a review"],"prefix":"10.22331","volume":"7","author":[{"given":"Ignatius W.","family":"Primaatmaja","sequence":"first","affiliation":[{"name":"Department of Electrical & Computer Engineering, National University of Singapore, Singapore"},{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Koon Tong","family":"Goh","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, National University of Singapore, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ernest Y.-Z.","family":"Tan","sequence":"additional","affiliation":[{"name":"Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John T.-F.","family":"Khoo","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, National University of Singapore, Singapore"},{"name":"Department of Computer Science, National University of Singapore, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shouvik","family":"Ghorai","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, National University of Singapore, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles C.-W.","family":"Lim","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, National University of Singapore, Singapore"},{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore"},{"name":"Global Technology Applied Research, JPMorgan Chase & Co, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,3,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. Ac\u00edn, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett., 98: 230501, Jun 2007. 10.1103\/PhysRevLett.98.230501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.98.230501.","DOI":"10.1103\/PhysRevLett.98.230501"},{"key":"1","doi-asserted-by":"publisher","unstructured":"R. Ahlswede and I. Csiszar. Common randomness in information theory and cryptography. i. secret sharing. IEEE Transactions on Information Theory, 39 (4): 1121\u20131132, 1993. 10.1109\/18.243431.","DOI":"10.1109\/18.243431"},{"key":"2","doi-asserted-by":"publisher","unstructured":"R. Arnon-Friedman and F. Leditzky. Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture. IEEE Transactions on Information Theory, 67 (10): 6606\u20136618, Oct 2021. 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URL https:\/\/doi.org\/10.1103\/PhysRevA.75.012334.","DOI":"10.1103\/PhysRevA.75.012334"},{"key":"6","doi-asserted-by":"publisher","unstructured":"J. Barrett, L. Hardy, and A. Kent. No signaling and quantum key distribution. Phys. Rev. Lett., 95: 010503, Jun 2005. 10.1103\/PhysRevLett.95.010503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.95.010503.","DOI":"10.1103\/PhysRevLett.95.010503"},{"key":"7","doi-asserted-by":"publisher","unstructured":"J. Barrett, R. Colbeck, and A. Kent. Memory attacks on device-independent quantum cryptography. Phys. Rev. Lett., 110: 010503, Jan 2013. 10.1103\/PhysRevLett.110.010503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.110.010503.","DOI":"10.1103\/PhysRevLett.110.010503"},{"key":"8","doi-asserted-by":"crossref","unstructured":"J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1 (3): 195, 1964.","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195"},{"key":"9","doi-asserted-by":"crossref","unstructured":"J. S. Bell. Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge University Press, 2004.","DOI":"10.1017\/CBO9780511815676"},{"key":"10","doi-asserted-by":"publisher","unstructured":"M. Ben-Or, M. Horodecki, D. W. Leung, D. Mayers, and J. Oppenheim. The universal composable security of quantum key distribution. In Theory of Cryptography, pages 386\u2013406. Springer Berlin Heidelberg, 2005. 10.1007\/978-3-540-30576-7_21. URL https:\/\/doi.org\/10.1007\/978-3-540-30576-7_21.","DOI":"10.1007\/978-3-540-30576-7_21"},{"key":"11","unstructured":"C. H. Bennett and G. Brassard. Quantum cryptography. In Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing, Bangalore, India, pages 175\u2013179, 1984."},{"key":"12","doi-asserted-by":"publisher","unstructured":"C. H. Bennett, G. Brassard, and N. D. Mermin. Quantum cryptography without Bell&apos;s theorem. Phys. Rev. Lett., 68: 557\u2013559, Feb 1992. 10.1103\/PhysRevLett.68.557. URL https:\/\/doi.org\/10.1103\/PhysRevLett.68.557.","DOI":"10.1103\/PhysRevLett.68.557"},{"key":"13","doi-asserted-by":"publisher","unstructured":"R. Bhavsar, S. Ragy, and R. Colbeck. Improved device-independent randomness expansion rates from tight bounds on the two sided randomness using CHSH tests. arXiv preprint arXiv:2103.07504, 2021. 10.48550\/arXiv.2103.07504. URL https:\/\/doi.org\/10.48550\/arXiv.2103.07504.","DOI":"10.48550\/arXiv.2103.07504"},{"key":"14","doi-asserted-by":"publisher","unstructured":"P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, et al. Experimentally generated randomness certified by the impossibility of superluminal signals. Nature, 556 (7700): 223\u2013226, 2018. 10.1038\/s41586-018-0019-0. URL https:\/\/doi.org\/10.1038\/s41586-018-0019-0.","DOI":"10.1038\/s41586-018-0019-0"},{"key":"15","doi-asserted-by":"publisher","unstructured":"C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. 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Journal of Computer and System Sciences, 18 (2): 143\u2013154, 1979. ISSN 0022-0000. https:\/\/doi.org\/10.1016\/0022-0000(79)90044-8. URL https:\/\/www.sciencedirect.com\/science\/article\/pii\/0022000079900448.","DOI":"10.1016\/0022-0000(79)90044-8"},{"key":"22","doi-asserted-by":"publisher","unstructured":"H. F. Chau. Practical scheme to share a secret key through a quantum channel with a 27.6% bit-error rate. Phys. Rev. A, 66: 060302, Dec 2002. 10.1103\/PhysRevA.66.060302. URL https:\/\/doi.org\/10.1103\/PhysRevA.66.060302.","DOI":"10.1103\/PhysRevA.66.060302"},{"key":"23","doi-asserted-by":"publisher","unstructured":"M. Christandl and R. Ferrara. Private states, quantum data hiding, and the swapping of perfect secrecy. Phys. Rev. Lett., 119: 220506, Nov 2017. 10.1103\/PhysRevLett.119.220506. URL https:\/\/doi.org\/10.1103\/PhysRevLett.119.220506.","DOI":"10.1103\/PhysRevLett.119.220506"},{"key":"24","doi-asserted-by":"crossref","unstructured":"M. Christandl, A. Ekert, M. Horodecki, P. Horodecki, J. Oppenheim, and R. Renner. Unifying classical and quantum key distillation. In S. P. Vadhan, editor, Theory of Cryptography, pages 456\u2013478, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-70936-7.","DOI":"10.1007\/978-3-540-70936-7_25"},{"key":"25","doi-asserted-by":"publisher","unstructured":"M. Christandl, R. Ferrara, and K. Horodecki. Upper bounds on device-independent quantum key distribution. Phys. Rev. Lett., 126: 160501, Apr 2021. 10.1103\/PhysRevLett.126.160501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.126.160501.","DOI":"10.1103\/PhysRevLett.126.160501"},{"key":"26","doi-asserted-by":"publisher","unstructured":"J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23: 880\u2013884, Oct 1969. 10.1103\/PhysRevLett.23.880. URL https:\/\/doi.org\/10.1103\/PhysRevLett.23.880.","DOI":"10.1103\/PhysRevLett.23.880"},{"key":"27","doi-asserted-by":"publisher","unstructured":"A. Coladangelo and J. Stark. Unconditional separation of finite and infinite-dimensional quantum correlations. arXiv preprint arXiv:1804.05116, 2018. 10.48550\/arXiv.1804.05116. URL https:\/\/doi.org\/10.48550\/arXiv.1804.05116.","DOI":"10.48550\/arXiv.1804.05116"},{"key":"28","doi-asserted-by":"publisher","unstructured":"P. J. Coles, E. M. Metodiev, and N. L\u00fctkenhaus. Numerical approach for unstructured quantum key distribution. Nature Communications, 7 (11712): 1\u20139, 2016. 10.1038\/ncomms11712. URL https:\/\/doi.org\/10.1038\/ncomms11712.","DOI":"10.1038\/ncomms11712"},{"key":"29","doi-asserted-by":"publisher","unstructured":"P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner. Entropic uncertainty relations and their applications. Rev. Mod. Phys., 89: 015002, Feb 2017. 10.1103\/RevModPhys.89.015002. URL https:\/\/doi.org\/10.1103\/RevModPhys.89.015002.","DOI":"10.1103\/RevModPhys.89.015002"},{"key":"30","doi-asserted-by":"publisher","unstructured":"I. Csiszar and J. Korner. Broadcast channels with confidential messages. IEEE Transactions on Information Theory, 24 (3): 339\u2013348, 1978. 10.1109\/TIT.1978.1055892.","DOI":"10.1109\/TIT.1978.1055892"},{"key":"31","doi-asserted-by":"publisher","unstructured":"M. Curty and H.-K. Lo. Foiling covert channels and malicious classical post-processing units in quantum key distribution. npj Quantum Information, 5 (14): 1\u201311, 2019. 10.1038\/s41534-019-0131-5.","DOI":"10.1038\/s41534-019-0131-5"},{"key":"32","doi-asserted-by":"publisher","unstructured":"M. Curty and T. Moroder. Heralded-qubit amplifiers for practical device-independent quantum key distribution. Phys. Rev. A, 84: 010304, Jul 2011. 10.1103\/PhysRevA.84.010304. URL https:\/\/doi.org\/10.1103\/PhysRevA.84.010304.","DOI":"10.1103\/PhysRevA.84.010304"},{"key":"33","doi-asserted-by":"publisher","unstructured":"S. Datta, H. Kampermann, and D. Bru\u00df. Device-independent secret key rates via a post-selected Bell inequality. arXiv preprint arXiv:2111.04482, 2021. 10.48550\/arXiv.2111.04482. URL https:\/\/doi.org\/10.48550\/arXiv.2111.04482.","DOI":"10.48550\/arXiv.2111.04482"},{"key":"34","doi-asserted-by":"crossref","unstructured":"P. J. Davis and P. Rabinowitz. Methods Of Numerical Integration. Academic Press, 2nd edition, 1984. ISBN 9781483264288.","DOI":"10.1016\/B978-0-12-206360-2.50012-1"},{"key":"35","doi-asserted-by":"publisher","unstructured":"I. Devetak and A. Winter. Distillation of secret key and entanglement from quantum states. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2053): 207\u2013235, 2005. 10.1098\/rspa.2004.1372. URL https:\/\/doi.org\/10.1098\/rspa.2004.1372.","DOI":"10.1098\/rspa.2004.1372"},{"key":"36","doi-asserted-by":"publisher","unstructured":"P. Divi\u00e1nszky, E. Bene, and T. V\u00e9rtesi. Qutrit witness from the grothendieck constant of order four. Phys. Rev. A, 96: 012113, Jul 2017. 10.1103\/PhysRevA.96.012113. URL https:\/\/doi.org\/10.1103\/PhysRevA.96.012113.","DOI":"10.1103\/PhysRevA.96.012113"},{"key":"37","doi-asserted-by":"publisher","unstructured":"F. Dupuis and O. Fawzi. Entropy accumulation with improved second-order term. IEEE Transactions on Information Theory, 65 (11): 7596\u20137612, 2019. 10.1109\/TIT.2019.2929564. URL https:\/\/doi.org\/10.1109\/TIT.2019.2929564.","DOI":"10.1109\/TIT.2019.2929564"},{"key":"38","doi-asserted-by":"publisher","unstructured":"F. Dupuis, O. Fawzi, and R. Renner. Entropy accumulation. Communications in Mathematical Physics, 379 (3): 867\u2013913, 2020. 10.1007\/s00220-020-03839-5. URL https:\/\/doi.org\/10.1007\/s00220-020-03839-5.","DOI":"10.1007\/s00220-020-03839-5"},{"key":"39","doi-asserted-by":"publisher","unstructured":"A. K. Ekert. Quantum cryptography based on Bell&apos;s theorem. Phys. Rev. Lett., 67: 661\u2013663, Aug 1991. 10.1103\/PhysRevLett.67.661. URL https:\/\/doi.org\/10.1103\/PhysRevLett.67.661.","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"40","doi-asserted-by":"publisher","unstructured":"M. Farkas, M. Balanz\u00f3-Juand\u00f3, K. \u0141ukanowski, J. Ko\u0142ody\u0144ski, and A. Ac\u00edn. Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols. Phys. Rev. Lett., 127: 050503, Jul 2021. 10.1103\/PhysRevLett.127.050503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.127.050503.","DOI":"10.1103\/PhysRevLett.127.050503"},{"key":"41","doi-asserted-by":"publisher","unstructured":"T. Fritz. Tsirelson&apos;s problem and Kirchberg&apos;s conjecture. Reviews in Mathematical Physics, 24 (05): 1250012, 2012. 10.1142\/S0129055X12500122. URL https:\/\/doi.org\/10.1142\/S0129055X12500122.","DOI":"10.1142\/S0129055X12500122"},{"key":"42","doi-asserted-by":"publisher","unstructured":"N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy. Trojan-horse attacks on quantum-key-distribution systems. Phys. Rev. A, 73: 022320, Feb 2006. 10.1103\/PhysRevA.73.022320. URL https:\/\/doi.org\/10.1103\/PhysRevA.73.022320.","DOI":"10.1103\/PhysRevA.73.022320"},{"key":"43","doi-asserted-by":"publisher","unstructured":"N. Gisin, S. Pironio, and N. Sangouard. Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier. Phys. Rev. Lett., 105: 070501, Aug 2010. 10.1103\/PhysRevLett.105.070501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.105.070501.","DOI":"10.1103\/PhysRevLett.105.070501"},{"key":"44","doi-asserted-by":"publisher","unstructured":"M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abell\u00e1n, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger. Significant-loophole-free test of Bell&apos;s theorem with entangled photons. Phys. Rev. Lett., 115: 250401, Dec 2015. 10.1103\/PhysRevLett.115.250401. URL https:\/\/doi.org\/10.1103\/PhysRevLett.115.250401.","DOI":"10.1103\/PhysRevLett.115.250401"},{"key":"45","doi-asserted-by":"publisher","unstructured":"K. T. Goh, J.-D. Bancal, and V. Scarani. Measurement-device-independent quantification of entanglement for given Hilbert space dimension. New Journal of Physics, 18 (4): 045022, Apr 2016. 10.1088\/1367-2630\/18\/4\/045022. URL https:\/\/doi.org\/10.1088\/1367-2630\/18\/4\/045022.","DOI":"10.1088\/1367-2630\/18\/4\/045022"},{"key":"46","doi-asserted-by":"publisher","unstructured":"J. R. Gonzales-Ureta, A. Predojevi\u0107, and A. Cabello. Device-independent quantum key distribution based on bell inequalities with more than two inputs and two outputs. Phys. Rev. A, 103: 052436, May 2021. 10.1103\/PhysRevA.103.052436. URL https:\/\/doi.org\/10.1103\/PhysRevA.103.052436.","DOI":"10.1103\/PhysRevA.103.052436"},{"key":"47","doi-asserted-by":"publisher","unstructured":"D. Gottesman and H.-K. Lo. Proof of security of quantum key distribution with two-way classical communications. IEEE Transactions on Information Theory, 49 (2): 457\u2013475, 2003. 10.1109\/TIT.2002.807289. URL https:\/\/doi.org\/10.1109\/TIT.2002.807289.","DOI":"10.1109\/TIT.2002.807289"},{"key":"48","doi-asserted-by":"publisher","unstructured":"F. Grasselli, G. Murta, H. Kampermann, and D. Bru\u00df. Entropy bounds for multiparty device-independent cryptography. PRX Quantum, 2: 010308, Jan 2021. 10.1103\/PRXQuantum.2.010308. URL https:\/\/doi.org\/10.1103\/PRXQuantum.2.010308.","DOI":"10.1103\/PRXQuantum.2.010308"},{"key":"49","unstructured":"S. J. Harris and S. K. Pandey. Entanglement and Non-Locality (lecture notes), 2016. URL https:\/\/www.math.uwaterloo.ca\/ vpaulsen\/EntanglementAndNonlocality_LectureNotes_7.pdf."},{"key":"50","doi-asserted-by":"publisher","unstructured":"B. Hensen, H. Bernien, A. E. Dr\u00e9au, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abell\u00e1n, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526 (7575): 682\u2013686, 2015. 10.1038\/nature15759. URL https:\/\/doi.org\/10.1038\/nature15759.","DOI":"10.1038\/nature15759"},{"key":"51","doi-asserted-by":"publisher","unstructured":"M. Ho, P. Sekatski, E. Y.-Z. Tan, R. Renner, J.-D. Bancal, and N. Sangouard. Noisy preprocessing facilitates a photonic realization of device-independent quantum key distribution. Phys. Rev. Lett., 124: 230502, Jun 2020. 10.1103\/PhysRevLett.124.230502. 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URL https:\/\/dx.doi.org\/10.1088\/1367-2630\/ac71bc.","DOI":"10.1088\/1367-2630\/ac71bc"},{"key":"57","doi-asserted-by":"publisher","unstructured":"R. Jain and S. Kundu. A direct product theorem for quantum communication complexity with applications to device-independent QKD. arXiv preprint arXiv:2106.04299, 2021. 10.48550\/arXiv.2106.04299. URL https:\/\/doi.org\/10.48550\/arXiv.2106.04299.","DOI":"10.48550\/arXiv.2106.04299"},{"key":"58","doi-asserted-by":"publisher","unstructured":"R. Jain, C. A. Miller, and Y. Shi. Parallel device-independent quantum key distribution. IEEE Transactions on Information Theory, 66 (9): 5567\u20135584, 2020. 10.1109\/TIT.2020.2986740. URL https:\/\/doi.org\/10.1109\/TIT.2020.2986740.","DOI":"10.1109\/TIT.2020.2986740"},{"key":"59","doi-asserted-by":"publisher","unstructured":"Z. Ji, A. Natarajan, T. Vidick, J. Wright, and H. Yuen. MIP* = RE. Commun. ACM, 64 (11): 131\u2013138, oct 2021. ISSN 0001-0782. 10.1145\/3485628. URL https:\/\/doi.org\/10.1145\/3485628.","DOI":"10.1145\/3485628"},{"key":"60","doi-asserted-by":"publisher","unstructured":"N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D. J. Twitchen, M. Markham, and R. Hanson. Entanglement distillation between solid-state quantum network nodes. Science, 356 (6341): 928\u2013932, 2017. 10.1126\/science.aan0070. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/science.aan0070.","DOI":"10.1126\/science.aan0070"},{"key":"61","doi-asserted-by":"publisher","unstructured":"E. Kaur, M. M. Wilde, and A. Winter. Fundamental limits on key rates in device-independent quantum key distribution. New Journal of Physics, 22 (2): 023039, feb 2020. 10.1088\/1367-2630\/ab6eaa. URL https:\/\/doi.org\/10.1088\/1367-2630\/ab6eaa.","DOI":"10.1088\/1367-2630\/ab6eaa"},{"key":"62","doi-asserted-by":"publisher","unstructured":"E. Kaur, K. Horodecki, and S. Das. Upper bounds on device-independent quantum key distribution rates in static and dynamic scenarios. Phys. Rev. Appl., 18: 054033, Nov 2022. 10.1103\/PhysRevApplied.18.054033. URL https:\/\/doi.org\/10.1103\/PhysRevApplied.18.054033.","DOI":"10.1103\/PhysRevApplied.18.054033"},{"key":"63","doi-asserted-by":"publisher","unstructured":"S. Khatri and N. L\u00fctkenhaus. Numerical evidence for bound secrecy from two-way postprocessing in quantum key distribution. Phys. Rev. A, 95: 042320, Apr 2017. 10.1103\/PhysRevA.95.042320. URL https:\/\/doi.org\/10.1103\/PhysRevA.95.042320.","DOI":"10.1103\/PhysRevA.95.042320"},{"key":"64","doi-asserted-by":"publisher","unstructured":"E. Knill, Y. Zhang, and H. Fu. Quantum probability estimation for randomness with quantum side information. arXiv preprint arXiv:1806.04553, 2018. 10.48550\/arXiv.1806.04553. URL https:\/\/doi.org\/10.48550\/arXiv.1806.04553.","DOI":"10.48550\/arXiv.1806.04553"},{"key":"65","doi-asserted-by":"publisher","unstructured":"M. Koashi. Simple security proof of quantum key distribution based on complementarity. New Journal of Physics, 11 (4): 045018, apr 2009. 10.1088\/1367-2630\/11\/4\/045018. URL https:\/\/doi.org\/10.1088\/1367-2630\/11\/4\/045018.","DOI":"10.1088\/1367-2630\/11\/4\/045018"},{"key":"66","doi-asserted-by":"publisher","unstructured":"J. Ko\u0142ody\u0144ski, A. M\u00e1ttar, P. Skrzypczyk, E. Woodhead, D. Cavalcanti, K. Banaszek, and A. Ac\u00edn. Device-independent quantum key distribution with single-photon sources. Quantum, 4: 260, Apr. 2020. ISSN 2521-327X. 10.22331\/q-2020-04-30-260. URL https:\/\/doi.org\/10.22331\/q-2020-04-30-260.","DOI":"10.22331\/q-2020-04-30-260"},{"key":"67","doi-asserted-by":"publisher","unstructured":"B. Kraus, N. Gisin, and R. Renner. Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett., 95: 080501, Aug 2005. 10.1103\/PhysRevLett.95.080501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.95.080501.","DOI":"10.1103\/PhysRevLett.95.080501"},{"key":"68","doi-asserted-by":"publisher","unstructured":"J.-\u00c5. Larsson. Loopholes in Bell inequality tests of local realism. Journal of Physics A: Mathematical and Theoretical, 47 (42): 424003, Oct 2014. 10.1088\/1751-8113\/47\/42\/424003. URL https:\/\/doi.org\/10.1088\/1751-8113\/47\/42\/424003.","DOI":"10.1088\/1751-8113\/47\/42\/424003"},{"key":"69","doi-asserted-by":"publisher","unstructured":"M.-H. Li, C. Wu, Y. Zhang, W.-Z. Liu, B. Bai, Y. Liu, W. Zhang, Q. Zhao, H. Li, Z. Wang, L. You, W. J. Munro, J. Yin, J. Zhang, C.-Z. Peng, X. Ma, Q. Zhang, J. Fan, and J.-W. Pan. Test of local realism into the past without detection and locality loopholes. Phys. Rev. Lett., 121: 080404, Aug 2018. 10.1103\/PhysRevLett.121.080404. URL https:\/\/doi.org\/10.1103\/PhysRevLett.121.080404.","DOI":"10.1103\/PhysRevLett.121.080404"},{"key":"70","doi-asserted-by":"publisher","unstructured":"M.-H. Li, X. Zhang, W.-Z. Liu, S.-R. Zhao, B. Bai, Y. Liu, Q. Zhao, Y. Peng, J. Zhang, Y. Zhang, W. J. Munro, X. Ma, Q. Zhang, J. Fan, and J.-W. Pan. Experimental realization of device-independent quantum randomness expansion. Phys. Rev. Lett., 126: 050503, Feb 2021. 10.1103\/PhysRevLett.126.050503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.126.050503.","DOI":"10.1103\/PhysRevLett.126.050503"},{"key":"71","doi-asserted-by":"publisher","unstructured":"C. C. W. Lim, C. Portmann, M. Tomamichel, R. Renner, and N. Gisin. Device-independent quantum key distribution with local Bell test. Phys. Rev. X, 3: 031006, Jul 2013. 10.1103\/PhysRevX.3.031006. URL https:\/\/doi.org\/10.1103\/PhysRevX.3.031006.","DOI":"10.1103\/PhysRevX.3.031006"},{"key":"72","doi-asserted-by":"publisher","unstructured":"W.-Z. Liu, M.-H. Li, S. Ragy, S.-R. Zhao, B. Bai, Y. Liu, P. J. Brown, J. Zhang, R. Colbeck, J. Fan, et al. Device-independent randomness expansion against quantum side information. Nature Physics, 17 (4): 448\u2013451, 2021. 10.1038\/s41567-020-01147-2. URL https:\/\/doi.org\/10.1038\/s41567-020-01147-2.","DOI":"10.1038\/s41567-020-01147-2"},{"key":"73","doi-asserted-by":"publisher","unstructured":"W.-Z. Liu, Y.-Z. Zhang, Y.-Z. Zhen, M.-H. Li, Y. Liu, J. Fan, F. Xu, Q. Zhang, and J.-W. Pan. Toward a photonic demonstration of device-independent quantum key distribution. Phys. Rev. Lett., 129: 050502, Jul 2022. 10.1103\/PhysRevLett.129.050502. URL https:\/\/doi.org\/10.1103\/PhysRevLett.129.050502.","DOI":"10.1103\/PhysRevLett.129.050502"},{"key":"74","doi-asserted-by":"publisher","unstructured":"Y. Liu, X. Yuan, M.-H. Li, W. Zhang, Q. Zhao, J. Zhong, Y. Cao, Y.-H. Li, L.-K. Chen, H. Li, T. Peng, Y.-A. Chen, C.-Z. Peng, S.-C. Shi, Z. Wang, L. You, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan. High-speed device-independent quantum random number generation without a detection loophole. Phys. Rev. Lett., 120: 010503, Jan 2018a. 10.1103\/PhysRevLett.120.010503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.120.010503.","DOI":"10.1103\/PhysRevLett.120.010503"},{"key":"75","doi-asserted-by":"publisher","unstructured":"Y. Liu, Q. Zhao, M.-H. Li, J.-Y. Guan, Y. Zhang, B. Bai, W. Zhang, W.-Z. Liu, C. Wu, X. Yuan, et al. Device-independent quantum random-number generation. Nature, 562 (7728): 548\u2013551, 2018b. 10.1038\/s41586-018-0559-3. URL https:\/\/doi.org\/10.1038\/s41586-018-0559-3.","DOI":"10.1038\/s41586-018-0559-3"},{"key":"76","doi-asserted-by":"publisher","unstructured":"H.-K. Lo, H. F. Chau, and M. Ardehali. Efficient quantum key distribution scheme and a proof of its unconditional security. Journal of Cryptology, 18 (2): 133\u2013165, 2005. 10.1007\/s00145-004-0142-y. URL https:\/\/doi.org\/10.1007\/s00145-004-0142-y.","DOI":"10.1007\/s00145-004-0142-y"},{"key":"77","doi-asserted-by":"publisher","unstructured":"H.-K. Lo, M. Curty, and B. Qi. Measurement-device-independent quantum key distribution. Phys. Rev. Lett., 108: 130503, Mar 2012. 10.1103\/PhysRevLett.108.130503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.108.130503.","DOI":"10.1103\/PhysRevLett.108.130503"},{"key":"78","doi-asserted-by":"publisher","unstructured":"K. \u0141ukanowski, M. Balanz\u00f3-Juand\u00f3, M. Farkas, A. Ac\u00edn, and J. Ko\u0142ody\u0144ski. Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks. arXiv preprint arXiv:2206.06245, 2022. 10.48550\/arXiv.2206.06245. URL https:\/\/arxiv.org\/abs\/2206.06245.","DOI":"10.48550\/arXiv.2206.06245"},{"key":"79","doi-asserted-by":"publisher","unstructured":"L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov. Hacking commercial quantum cryptography systems by tailored bright illumination. Nature Photonics, 4 (10): 686\u2013689, 2010. 10.1038\/nphoton.2010.214. URL https:\/\/doi.org\/10.1038\/nphoton.2010.214.","DOI":"10.1038\/nphoton.2010.214"},{"key":"80","doi-asserted-by":"publisher","unstructured":"X. Ma and N. L\u00fctkenhaus. Improved data post-processing in quantum key distribution and application to loss thresholds in device-independent QKD. Quantum Info. Comput., 12 (3\u20134): 203\u2013214, Mar 2012. ISSN 1533-7146. 10.26421\/QIC12.3-4-2. URL https:\/\/doi.org\/10.26421\/QIC12.3-4-2.","DOI":"10.26421\/QIC12.3-4-2"},{"key":"81","doi-asserted-by":"publisher","unstructured":"X. Ma, C.-H. F. Fung, F. Dupuis, K. Chen, K. Tamaki, and H.-K. Lo. Decoy-state quantum key distribution with two-way classical postprocessing. Phys. Rev. A, 74: 032330, Sep 2006. 10.1103\/PhysRevA.74.032330. URL https:\/\/doi.org\/10.1103\/PhysRevA.74.032330.","DOI":"10.1103\/PhysRevA.74.032330"},{"key":"82","doi-asserted-by":"publisher","unstructured":"V. Makarov. Controlling passively quenched single photon detectors by bright light. New Journal of Physics, 11 (6): 065003, Jun 2009. 10.1088\/1367-2630\/11\/6\/065003. URL https:\/\/doi.org\/10.1088\/1367-2630\/11\/6\/065003.","DOI":"10.1088\/1367-2630\/11\/6\/065003"},{"key":"83","doi-asserted-by":"publisher","unstructured":"M. Masini, S. Pironio, and E. Woodhead. Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints. Quantum, 6: 843, Oct. 2022. ISSN 2521-327X. 10.22331\/q-2022-10-20-843. URL https:\/\/doi.org\/10.22331\/q-2022-10-20-843.","DOI":"10.22331\/q-2022-10-20-843"},{"key":"84","doi-asserted-by":"publisher","unstructured":"D. Mayers and A. Yao. Quantum cryptography with imperfect apparatus. In Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), pages 503\u2013509, 1998. 10.1109\/SFCS.1998.743501.","DOI":"10.1109\/SFCS.1998.743501"},{"key":"85","doi-asserted-by":"crossref","unstructured":"D. Mayers and A. Yao. Self testing quantum apparatus. Quantum Info. Comput., 4 (4): 273\u2013286, jul 2004. ISSN 1533-7146. URL https:\/\/dl.acm.org\/doi\/10.5555\/2011827.2011830.","DOI":"10.26421\/QIC4.4-3"},{"key":"86","doi-asserted-by":"publisher","unstructured":"T. Metger and R. Renner. Security of quantum key distribution from generalised entropy accumulation. arXiv preprint arXiv:2203.04993, 2022. URL https:\/\/doi.org\/10.48550\/arXiv.2203.04993.","DOI":"10.48550\/arXiv.2203.04993"},{"key":"87","doi-asserted-by":"publisher","unstructured":"T. Metger, Y. Dulek, A. Coladangelo, and R. Arnon-Friedman. Device-independent quantum key distribution from computational assumptions. New Journal of Physics, 23 (12): 123021, Dec 2021. 10.1088\/1367-2630\/ac304b. URL https:\/\/doi.org\/10.1088\/1367-2630\/ac304b.","DOI":"10.1088\/1367-2630\/ac304b"},{"key":"88","doi-asserted-by":"publisher","unstructured":"T. Metger, O. Fawzi, D. Sutter, and R. Renner. Generalised entropy accumulation. arXiv preprint arXiv:2203.04989, 2022. 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Quantum conference key agreement: A review. Advanced Quantum Technologies, 3 (11): 2000025, 2020. https:\/\/doi.org\/10.1002\/qute.202000025. URL https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1002\/qute.202000025.","DOI":"10.1002\/qute.202000025"},{"key":"93","doi-asserted-by":"publisher","unstructured":"D. Nadlinger, P. Drmota, B. Nichol, G. Araneda, D. Main, R. Srinivas, D. Lucas, C. Ballance, K. Ivanov, E.-Z. Tan, et al. Experimental quantum key distribution certified by Bell&apos;s theorem. Nature, 607 (7920): 682\u2013686, 2022. 10.1038\/s41586-022-04941-5. URL https:\/\/doi.org\/10.1038\/s41586-022-04941-5.","DOI":"10.1038\/s41586-022-04941-5"},{"key":"94","doi-asserted-by":"publisher","unstructured":"Y. Nagamatsu, A. Mizutani, R. Ikuta, T. Yamamoto, N. Imoto, and K. Tamaki. Security of quantum key distribution with light sources that are not independently and identically distributed. Phys. Rev. A, 93: 042325, Apr 2016. 10.1103\/PhysRevA.93.042325. URL https:\/\/doi.org\/10.1103\/PhysRevA.93.042325.","DOI":"10.1103\/PhysRevA.93.042325"},{"key":"95","doi-asserted-by":"publisher","unstructured":"A. Navarrete, M. Pereira, M. Curty, and K. Tamaki. Practical quantum key distribution that is secure against side channels. Phys. Rev. Applied, 15: 034072, Mar 2021. 10.1103\/PhysRevApplied.15.034072. URL https:\/\/doi.org\/10.1103\/PhysRevApplied.15.034072.","DOI":"10.1103\/PhysRevApplied.15.034072"},{"key":"96","doi-asserted-by":"publisher","unstructured":"M. Navascu\u00e9s, S. Pironio, and A. Ac\u00edn. Bounding the set of quantum correlations. Phys. Rev. Lett., 98: 010401, Jan 2007. 10.1103\/PhysRevLett.98.010401. URL https:\/\/doi.org\/10.1103\/PhysRevLett.98.010401.","DOI":"10.1103\/PhysRevLett.98.010401"},{"key":"97","doi-asserted-by":"publisher","unstructured":"M. Navascu\u00e9s, S. Pironio, and A. Ac\u00edn. A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. New Journal of Physics, 10 (7): 073013, jul 2008. 10.1088\/1367-2630\/10\/7\/073013. URL https:\/\/doi.org\/10.1088\/1367-2630\/10\/7\/073013.","DOI":"10.1088\/1367-2630\/10\/7\/073013"},{"key":"98","doi-asserted-by":"publisher","unstructured":"M. Navascu\u00e9s, T. Cooney, D. P\u00e9rez-Garc\u00eda, and N. Villanueva. A physical approach to Tsirelson&apos;s problem. Foundations of Physics, 42 (8): 985\u2013995, Aug 2012. ISSN 1572-9516. 10.1007\/s10701-012-9641-0. URL https:\/\/doi.org\/10.1007\/s10701-012-9641-0.","DOI":"10.1007\/s10701-012-9641-0"},{"key":"99","doi-asserted-by":"publisher","unstructured":"M. Paw\u0142owski and N. Brunner. Semi-device-independent security of one-way quantum key distribution. Phys. Rev. A, 84: 010302, Jul 2011. 10.1103\/PhysRevA.84.010302. URL https:\/\/doi.org\/10.1103\/PhysRevA.84.010302.","DOI":"10.1103\/PhysRevA.84.010302"},{"key":"100","doi-asserted-by":"publisher","unstructured":"P. M. Pearle. Hidden-variable example based upon data rejection. Phys. Rev. D, 2: 1418\u20131425, Oct 1970. 10.1103\/PhysRevD.2.1418. URL https:\/\/doi.org\/10.1103\/PhysRevD.2.1418.","DOI":"10.1103\/PhysRevD.2.1418"},{"key":"101","doi-asserted-by":"publisher","unstructured":"M. Pereira, G. Kato, A. Mizutani, M. Curty, and K. Tamaki. Quantum key distribution with correlated sources. Science Advances, 6 (37): eaaz4487, 2020. 10.1126\/sciadv.aaz4487. URL https:\/\/www.science.org\/doi\/abs\/10.1126\/sciadv.aaz4487.","DOI":"10.1126\/sciadv.aaz4487"},{"key":"102","doi-asserted-by":"publisher","unstructured":"F. A. P. Petitcolas. Kerckhoffs&apos; Principle, pages 675\u2013675. Springer US, Boston, MA, 2011. ISBN 978-1-4419-5906-5. 10.1007\/978-1-4419-5906-5_487. URL https:\/\/doi.org\/10.1007\/978-1-4419-5906-5_487.","DOI":"10.1007\/978-1-4419-5906-5_487"},{"key":"103","doi-asserted-by":"publisher","unstructured":"S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi. Fundamental limits of repeaterless quantum communications. Nature Communications, 8 (15043): 1\u201315, 2017. URL https:\/\/doi.org\/10.1038\/ncomms15043.","DOI":"10.1038\/ncomms15043"},{"key":"104","doi-asserted-by":"publisher","unstructured":"S. Pironio, A. Ac\u00edn, N. Brunner, N. Gisin, S. Massar, and V. Scarani. Device-independent quantum key distribution secure against collective attacks. New Journal of Physics, 11 (4): 045021, 2009. URL https:\/\/doi.org\/10.1088\/\u200b1367-2630\/\u200b11\/\u200b4\/\u200b045021.","DOI":"10.1088\/\u200b1367-2630\/\u200b11\/\u200b4\/\u200b045021"},{"key":"105","doi-asserted-by":"publisher","unstructured":"S. Pironio, M. Navascu\u00e9s, and A. Ac\u00edn. Convergent relaxations of polynomial optimization problems with noncommuting variables. SIAM Journal on Optimization, 20 (5): 2157\u20132180, 2010. URL https:\/\/doi.org\/10.1137\/090760155.","DOI":"10.1137\/090760155"},{"key":"106","doi-asserted-by":"publisher","unstructured":"D. Pitkanen, X. Ma, R. Wickert, P. van Loock, and N. L\u00fctkenhaus. Efficient heralding of photonic qubits with applications to device-independent quantum key distribution. Phys. Rev. A, 84: 022325, Aug 2011. 10.1103\/PhysRevA.84.022325. URL https:\/\/doi.org\/10.1103\/PhysRevA.84.022325.","DOI":"10.1103\/PhysRevA.84.022325"},{"key":"107","unstructured":"C. Portmann and R. Renner. Cryptographic security of quantum key distribution. arXiv preprint arXiv:1409.3525, 2014. URL https:\/\/arxiv.org\/abs\/1409.3525."},{"key":"108","doi-asserted-by":"publisher","unstructured":"C. Portmann and R. Renner. Security in Quantum Cryptography. arXiv preprint arXiv:2102.00021, 2021. URL https:\/\/doi.org\/10.1103\/RevModPhys.94.025008.","DOI":"10.1103\/RevModPhys.94.025008"},{"key":"109","doi-asserted-by":"publisher","unstructured":"R. Rahaman, M. G. Parker, P. Mironowicz, and M. Paw\u0142owski. Device-independent quantum key distribution based on measurement inputs. Phys. Rev. A, 92: 062304, Dec 2015. 10.1103\/PhysRevA.92.062304. 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Wehner. Fully device-independent conference key agreement. Phys. Rev. A, 97: 022307, Feb 2018. 10.1103\/PhysRevA.97.022307. URL https:\/\/doi.org\/10.1103\/PhysRevA.97.022307.","DOI":"10.1103\/PhysRevA.97.022307"},{"key":"114","doi-asserted-by":"publisher","unstructured":"W. Rosenfeld, D. Burchardt, R. Garthoff, K. Redeker, N. Ortegel, M. Rau, and H. Weinfurter. Event-ready Bell test using entangled atoms simultaneously closing detection and locality loopholes. Phys. Rev. Lett., 119: 010402, Jul 2017. 10.1103\/PhysRevLett.119.010402. URL https:\/\/doi.org\/10.1103\/PhysRevLett.119.010402.","DOI":"10.1103\/PhysRevLett.119.010402"},{"key":"115","doi-asserted-by":"crossref","unstructured":"V. Scarani. Bell nonlocality. Oxford Graduate Texts, 2019.","DOI":"10.1093\/oso\/9780198788416.001.0001"},{"key":"116","doi-asserted-by":"publisher","unstructured":"V. Scarani and R. Renner. Security Bounds for Quantum Cryptography with Finite Resources. 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Randomness extraction from bell violation with continuous parametric down-conversion. Phys. Rev. Lett., 121: 150402, Oct 2018. 10.1103\/PhysRevLett.121.150402. URL https:\/\/doi.org\/10.1103\/PhysRevLett.121.150402.","DOI":"10.1103\/PhysRevLett.121.150402"},{"key":"126","doi-asserted-by":"publisher","unstructured":"P. W. Shor and J. Preskill. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett., 85: 441\u2013444, Jul 2000. 10.1103\/PhysRevLett.85.441. URL https:\/\/doi.org\/10.1103\/PhysRevLett.85.441.","DOI":"10.1103\/PhysRevLett.85.441"},{"key":"127","doi-asserted-by":"publisher","unstructured":"W. Slofstra. Tsirelson\u2019s problem and an embedding theorem for groups arising from non-local games. Journal of the American Mathematical Society, 33 (1): 1\u201356, 2020. 10.1090\/jams\/929. URL https:\/\/doi.org\/10.1090\/jams\/929.","DOI":"10.1090\/jams\/929"},{"key":"128","doi-asserted-by":"crossref","unstructured":"J. F. Sturm. 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Randomness in post-selected events. New Journal of Physics, 18 (3): 035007, mar 2016. 10.1088\/1367-2630\/18\/3\/035007. URL https:\/\/doi.org\/10.1088\/1367-2630\/18\/3\/035007.","DOI":"10.1088\/1367-2630\/18\/3\/035007"},{"key":"135","doi-asserted-by":"crossref","unstructured":"K.-C. Toh, M. J. Todd, and R. H. T\u00fct\u00fcnc\u00fc. SDPT3\u2014a MATLAB software package for semidefinite programming, version 1.3. Optimization methods and software, 11 (1-4): 545\u2013581, 1999.","DOI":"10.1080\/10556789908805762"},{"key":"136","doi-asserted-by":"publisher","unstructured":"M. Tomamichel and E. H\u00e4nggi. The link between entropic uncertainty and nonlocality. Journal of Physics A: Mathematical and Theoretical, 46 (5): 055301, jan 2013. 10.1088\/1751-8113\/46\/5\/055301. URL https:\/\/doi.org\/10.1088\/1751-8113\/46\/5\/055301.","DOI":"10.1088\/1751-8113\/46\/5\/055301"},{"key":"137","doi-asserted-by":"publisher","unstructured":"M. Tomamichel and A. Leverrier. A largely self-contained and complete security proof for quantum key distribution. Quantum, 1: 14, July 2017. ISSN 2521-327X. 10.22331\/q-2017-07-14-14. URL https:\/\/doi.org\/10.22331\/q-2017-07-14-14.","DOI":"10.22331\/q-2017-07-14-14"},{"key":"138","doi-asserted-by":"publisher","unstructured":"M. Tomamichel, R. Colbeck, and R. Renner. A fully quantum asymptotic equipartition property. IEEE Transactions on Information Theory, 55 (12): 5840\u20135847, 2009. 10.1109\/TIT.2009.2032797.","DOI":"10.1109\/TIT.2009.2032797"},{"key":"139","doi-asserted-by":"publisher","unstructured":"M. Tomamichel, C. Schaffner, A. Smith, and R. Renner. Leftover hashing against quantum side information. IEEE Transactions on Information Theory, 57 (8): 5524\u20135535, 2011. 10.1109\/TIT.2011.2158473. URL https:\/\/doi.org\/10.1109\/TIT.2011.2158473.","DOI":"10.1109\/TIT.2011.2158473"},{"key":"140","doi-asserted-by":"publisher","unstructured":"M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner. Tight finite-key analysis for quantum cryptography. Nature Communications, 3 (634): 1\u20136, 2012. 10.1038\/ncomms1631. URL https:\/\/doi.org\/10.1038\/ncomms1631.","DOI":"10.1038\/ncomms1631"},{"key":"141","doi-asserted-by":"publisher","unstructured":"M. Tomamichel, J. Martinez-Mateo, C. Pacher, and D. Elkouss. Fundamental finite key limits for one-way information reconciliation in quantum key distribution. Quantum Information Processing, 16 (11): 280, Oct 2017. ISSN 1573-1332. 10.1007\/s11128-017-1709-5. URL https:\/\/doi.org\/10.1007\/s11128-017-1709-5.","DOI":"10.1007\/s11128-017-1709-5"},{"key":"142","doi-asserted-by":"publisher","unstructured":"B. Toner. Monogamy of non-local quantum correlations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465 (2101): 59\u201369, 2009. 10.1098\/rspa.2008.0149. URL https:\/\/royalsocietypublishing.org\/doi\/abs\/10.1098\/rspa.2008.0149.","DOI":"10.1098\/rspa.2008.0149"},{"key":"143","unstructured":"B. S. 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Van Himbeeck, E. Woodhead, N. J. Cerf, R. Garc\u00eda-Patr\u00f3n, and S. Pironio. Semi-device-independent framework based on natural physical assumptions. Quantum, 1: 33, Nov. 2017. ISSN 2521-327X. 10.22331\/q-2017-11-18-33. URL https:\/\/doi.org\/10.22331\/q-2017-11-18-33.","DOI":"10.22331\/q-2017-11-18-33"},{"key":"147","doi-asserted-by":"publisher","unstructured":"U. Vazirani and T. Vidick. Fully device-independent quantum key distribution. Phys. Rev. Lett., 113: 140501, Sep 2014. 10.1103\/PhysRevLett.113.140501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.113.140501.","DOI":"10.1103\/PhysRevLett.113.140501"},{"key":"148","doi-asserted-by":"publisher","unstructured":"T. Vidick. Parallel DIQKD from parallel repetition. arXiv preprint arXiv:1703.08508, 2017. 10.48550\/arXiv.1703.08508. URL https:\/\/doi.org\/10.48550\/arXiv.1703.08508.","DOI":"10.48550\/arXiv.1703.08508"},{"key":"149","doi-asserted-by":"publisher","unstructured":"V. C. Vivoli, P. Sekatski, J.-D. Bancal, C. Lim, B. Christensen, A. Martin, R. Thew, H. Zbinden, N. Gisin, and N. Sangouard. Challenging preconceptions about Bell tests with photon pairs. Phys. Rev. A, 91: 012107, Jan 2015a. 10.1103\/PhysRevA.91.012107. URL https:\/\/doi.org\/10.1103\/PhysRevA.91.012107.","DOI":"10.1103\/PhysRevA.91.012107"},{"key":"150","doi-asserted-by":"publisher","unstructured":"V. C. Vivoli, P. Sekatski, J.-D. Bancal, C. Lim, A. Martin, R. Thew, H. Zbinden, N. Gisin, and N. Sangouard. Comparing different approaches for generating random numbers device-independently using a photon pair source. New Journal of Physics, 17 (2): 023023, 2015b. 10.1088\/1367-2630\/17\/2\/023023. URL https:\/\/doi.org\/10.1088\/1367-2630\/17\/2\/023023.","DOI":"10.1088\/1367-2630\/17\/2\/023023"},{"key":"151","doi-asserted-by":"publisher","unstructured":"N. Walk, S. Hosseini, J. Geng, O. Thearle, J. Y. Haw, S. Armstrong, S. M. Assad, J. Janousek, T. C. Ralph, T. Symul, H. M. Wiseman, and P. K. Lam. Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution. Optica, 3 (6): 634\u2013642, Jun 2016. 10.1364\/OPTICA.3.000634. URL http:\/\/opg.optica.org\/optica\/abstract.cfm?URI=optica-3-6-634.","DOI":"10.1364\/OPTICA.3.000634"},{"key":"152","doi-asserted-by":"publisher","unstructured":"Y. Wang, I. W. Primaatmaja, E. Lavie, A. Varvitsiotis, and C. C. W. Lim. Characterising the correlations of prepare-and-measure quantum networks. npj Quantum Information, 5 (17): 1\u20136, 2019. 10.1038\/s41534-019-0133-3. URL https:\/\/doi.org\/10.1038\/s41534-019-0133-3.","DOI":"10.1038\/s41534-019-0133-3"},{"key":"153","doi-asserted-by":"publisher","unstructured":"S. Watanabe, R. Matsumoto, T. Uyematsu, and Y. Kawano. Key rate of quantum key distribution with hashed two-way classical communication. Phys. Rev. A, 76: 032312, Sep 2007. 10.1103\/PhysRevA.76.032312. URL https:\/\/doi.org\/10.1103\/PhysRevA.76.032312.","DOI":"10.1103\/PhysRevA.76.032312"},{"key":"154","doi-asserted-by":"publisher","unstructured":"M. N. Wegman and J. L. Carter. New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences, 22 (3): 265\u2013279, 1981. ISSN 0022-0000. https:\/\/doi.org\/10.1016\/0022-0000(81)90033-7. URL https:\/\/www.sciencedirect.com\/science\/article\/pii\/0022000081900337.","DOI":"10.1016\/0022-0000(81)90033-7"},{"key":"155","doi-asserted-by":"publisher","unstructured":"R. F. Werner. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40: 4277\u20134281, Oct 1989. 10.1103\/PhysRevA.40.4277. URL https:\/\/doi.org\/10.1103\/PhysRevA.40.4277.","DOI":"10.1103\/PhysRevA.40.4277"},{"key":"156","doi-asserted-by":"publisher","unstructured":"M. Winczewski, T. Das, and K. Horodecki. Limitations on device independent key secure against non signaling adversary via the squashed non-locality. arXiv preprint arXiv:1903.12154, 2019. 10.48550\/arXiv.1903.12154. URL https:\/\/arxiv.org\/abs\/1903.12154.","DOI":"10.48550\/arXiv.1903.12154"},{"key":"157","doi-asserted-by":"publisher","unstructured":"A. Winick, N. L\u00fctkenhaus, and P. J. Coles. Reliable numerical key rates for quantum key distribution. Quantum, 2: 77, July 2018. ISSN 2521-327X. 10.22331\/q-2018-07-26-77. URL https:\/\/doi.org\/10.22331\/q-2018-07-26-77.","DOI":"10.22331\/q-2018-07-26-77"},{"key":"158","doi-asserted-by":"publisher","unstructured":"E. Woodhead. Semi device independence of the BB84 protocol. New Journal of Physics, 18 (5): 055010, May 2016. 10.1088\/1367-2630\/18\/5\/055010. URL https:\/\/doi.org\/10.1088\/1367-2630\/18\/5\/055010.","DOI":"10.1088\/1367-2630\/18\/5\/055010"},{"key":"159","doi-asserted-by":"publisher","unstructured":"E. Woodhead and S. Pironio. Secrecy in prepare-and-measure Clauser-Horne-Shimony-Holt tests with a qubit bound. Phys. Rev. Lett., 115: 150501, Oct 2015. 10.1103\/PhysRevLett.115.150501. URL https:\/\/doi.org\/10.1103\/PhysRevLett.115.150501.","DOI":"10.1103\/PhysRevLett.115.150501"},{"key":"160","doi-asserted-by":"publisher","unstructured":"E. Woodhead, A. Ac\u00edn, and S. Pironio. Device-independent quantum key distribution with asymmetric CHSH inequalities. Quantum, 5: 443, Apr. 2021. ISSN 2521-327X. 10.22331\/q-2021-04-26-443. URL https:\/\/doi.org\/10.22331\/q-2021-04-26-443.","DOI":"10.22331\/q-2021-04-26-443"},{"key":"161","doi-asserted-by":"publisher","unstructured":"F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan. Secure quantum key distribution with realistic devices. Rev. Mod. Phys., 92: 025002, May 2020. 10.1103\/RevModPhys.92.025002. URL https:\/\/doi.org\/10.1103\/RevModPhys.92.025002.","DOI":"10.1103\/RevModPhys.92.025002"},{"key":"162","doi-asserted-by":"publisher","unstructured":"F. Xu, Y.-Z. Zhang, Q. Zhang, and J.-W. Pan. Device-independent quantum key distribution with random postselection. Phys. Rev. Lett., 128: 110506, Mar 2022. 10.1103\/PhysRevLett.128.110506. URL https:\/\/doi.org\/10.1103\/PhysRevLett.128.110506.","DOI":"10.1103\/PhysRevLett.128.110506"},{"key":"163","doi-asserted-by":"publisher","unstructured":"K.-i. Yoshino, M. Fujiwara, K. Nakata, T. Sumiya, T. Sasaki, M. Takeoka, M. Sasaki, A. Tajima, M. Koashi, and A. Tomita. Quantum key distribution with an efficient countermeasure against correlated intensity fluctuations in optical pulses. npj Quantum Information, 4 (8): 1\u20138, 2018. 10.1038\/s41534-017-0057-8. URL https:\/\/doi.org\/10.1038\/s41534-017-0057-8.","DOI":"10.1038\/s41534-017-0057-8"},{"key":"164","doi-asserted-by":"publisher","unstructured":"V. Zapatero and M. Curty. Long-distance device-independent quantum key distribution. Scientific Reports, 9 (17749): 1\u201318, 2019. 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Nature, 607 (7920): 687\u2013691, 2022. 10.1038\/s41586-022-04891-y. URL https:\/\/doi.org\/10.1038\/s41586-022-04891-y.","DOI":"10.1038\/s41586-022-04891-y"},{"key":"168","doi-asserted-by":"publisher","unstructured":"X. Zhang, P. Zeng, T. Ye, H.-K. Lo, and X. Ma. Quantum complementarity approach to device-independent security. arXiv preprint arXiv:2111.13855, 2021b. 10.48550\/arXiv.2111.13855. URL https:\/\/arxiv.org\/abs\/2111.13855.","DOI":"10.48550\/arXiv.2111.13855"},{"key":"169","doi-asserted-by":"publisher","unstructured":"Y. Zhang, H. Fu, and E. Knill. Efficient randomness certification by quantum probability estimation. Phys. Rev. Research, 2: 013016, Jan 2020a. 10.1103\/PhysRevResearch.2.013016. URL https:\/\/doi.org\/10.1103\/PhysRevResearch.2.013016.","DOI":"10.1103\/PhysRevResearch.2.013016"},{"key":"170","doi-asserted-by":"publisher","unstructured":"Y. Zhang, L. K. Shalm, J. C. Bienfang, M. J. Stevens, M. D. Mazurek, S. W. Nam, C. Abell\u00e1n, W. Amaya, M. W. Mitchell, H. Fu, C. A. Miller, A. Mink, and E. Knill. Experimental low-latency device-independent quantum randomness. Phys. Rev. Lett., 124: 010505, Jan 2020b. 10.1103\/PhysRevLett.124.010505. 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