{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T04:00:50Z","timestamp":1781582450674,"version":"3.54.5"},"reference-count":62,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T00:00:00Z","timestamp":1571875200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown. On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases. In this work we propose a novel family of Bell inequalities which exhibit precisely these properties, and whose maximal quantum violation can be computed analytically. In the simplest scenario it recovers the CHSH Bell inequality. These inequalities involve<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>measurements settings, each having<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>outcomes for an arbitrary prime number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:math>. We then show that in the three-outcome case our Bell inequality can be used to self-test the maximally entangled state of two-qutrits and three mutually unbiased bases at each site. Yet, we demonstrate that in the case of more outcomes, their maximal violation does not allow for self-testing in the standard sense, which motivates the definition of a new weak form of self-testing. The ability to certify high-dimensional MUBs makes these inequalities attractive from the device-independent cryptography point of view.<\/jats:p>","DOI":"10.22331\/q-2019-10-24-198","type":"journal-article","created":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T14:20:44Z","timestamp":1571926844000},"page":"198","source":"Crossref","is-referenced-by-count":60,"title":["Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems"],"prefix":"10.22331","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1133-3786","authenticated-orcid":false,"given":"J\u0119drzej","family":"Kaniewski","sequence":"first","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik\u00f3w 32\/46, 02-668 Warsaw, Poland"},{"name":"QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0361-6631","authenticated-orcid":false,"given":"Ivan","family":"\u0160upi\u0107","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6123-1422","authenticated-orcid":false,"given":"Jordi","family":"Tura","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, 85748 Garching, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3374-5968","authenticated-orcid":false,"given":"Flavio","family":"Baccari","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4548-4339","authenticated-orcid":false,"given":"Alexia","family":"Salavrakos","sequence":"additional","affiliation":[{"name":"ICFO-Institut de Ci\u00e8ncies Fot\u00f2niques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1154-6132","authenticated-orcid":false,"given":"Remigiusz","family":"Augusiak","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik\u00f3w 32\/46, 02-668 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"O. Andersson, P. Badzi\u0105g, I. Bengtsson, I. Dumitru, and A. Cabello. Self-testing properties of Gisin's elegant Bell inequality. Phys. Rev. A, 96: 032119, 2017. DOI:10.1103\/PhysRevA.96.032119.","DOI":"10.1103\/PhysRevA.96.032119"},{"key":"1","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, 2007. DOI:10.1103\/PhysRevLett.98.230501.","DOI":"10.1103\/PhysRevLett.98.230501"},{"key":"2","doi-asserted-by":"publisher","unstructured":"R. Arnon-Friedman, F. Dupuis, O. Fawzi, R. Renner, and T. Vidick. Practical device-independent quantum cryptography via entropy accumulation. Nat. Commun., 9: 459, 2018. DOI:10.1038\/s41467-017-02307-4.","DOI":"10.1038\/s41467-017-02307-4"},{"key":"3","doi-asserted-by":"publisher","unstructured":"A. Ac\u00edn, N. Gisin, and L. Masanes. From Bell's theorem to secure quantum key distribution. Phys. Rev. Lett., 97: 120405, 2006. DOI:10.1103\/PhysRevLett.97.120405.","DOI":"10.1103\/PhysRevLett.97.120405"},{"key":"4","doi-asserted-by":"publisher","unstructured":"A. Ac\u00edn, S. Massar, and S. Pironio. Randomness versus nonlocality and entanglement. Phys. Rev. Lett., 108: 100402, 2012. DOI:10.1103\/PhysRevLett.108.100402.","DOI":"10.1103\/PhysRevLett.108.100402"},{"key":"5","doi-asserted-by":"publisher","unstructured":"S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, and F. Vatan. A new proof for the existence of mutually unbiased bases. Algorithmica, 34: 512, 2002. DOI:10.1007\/s00453-002-0980-7.","DOI":"10.1007\/s00453-002-0980-7"},{"key":"6","doi-asserted-by":"publisher","unstructured":"N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner. Bell nonlocality. Rev. Mod. Phys., 86: 419, 2014. DOI:10.1103\/RevModPhys.86.419.","DOI":"10.1103\/RevModPhys.86.419"},{"key":"7","doi-asserted-by":"crossref","unstructured":"J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1: 195, 1964.","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195"},{"key":"8","doi-asserted-by":"publisher","unstructured":"J. Barrett, L. Hardy, and A. Kent. No signaling and quantum key distribution. Phys. Rev. Lett., 95: 010503, 2005. DOI:10.1103\/PhysRevLett.95.010503.","DOI":"10.1103\/PhysRevLett.95.010503"},{"key":"9","doi-asserted-by":"publisher","unstructured":"J. Barrett, A. Kent, and S. Pironio. Maximally nonlocal and monogamous quantum correlations. Phys. Rev. Lett., 97: 170409, 2006. DOI:10.1103\/PhysRevLett.97.170409.","DOI":"10.1103\/PhysRevLett.97.170409"},{"key":"10","doi-asserted-by":"publisher","unstructured":"C.-E. Bardyn, T. C. H. Liew, S. Massar, M. McKague, and V. Scarani. Device independent state estimation based on Bell's inequalities. Phys. Rev. A, 80: 062327, 2009. DOI:10.1103\/PhysRevA.80.062327.","DOI":"10.1103\/PhysRevA.80.062327"},{"key":"11","doi-asserted-by":"publisher","unstructured":"H. Buhrman and S. Massar. Causality and Tsirelson's bounds. Phys. Rev. A, 72: 052103, 2005. DOI:10.1103\/PhysRevA.72.052103.","DOI":"10.1103\/PhysRevA.72.052103"},{"key":"12","doi-asserted-by":"publisher","unstructured":"C. Bamps and S. Pironio. Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing. Phys. Rev. A, 91: 052111, 2015. DOI:10.1103\/PhysRevA.91.052111.","DOI":"10.1103\/PhysRevA.91.052111"},{"key":"13","doi-asserted-by":"publisher","unstructured":"N. Brunner, S. Pironio, A. Ac\u00edn, N. Gisin, A. A. M\u00e9thot, and V. Scarani. Testing the dimension of Hilbert spaces. Phys. Rev. Lett., 100: 210503, 2008. DOI:10.1103\/PhysRevLett.100.210503.","DOI":"10.1103\/PhysRevLett.100.210503"},{"key":"14","doi-asserted-by":"publisher","unstructured":"J. Bouda, M. Paw\u0142owski, M. Pivoluska, and M. Plesch. Device-independent randomness extraction from an arbitrarily weak min-entropy source. Phys. Rev. A, 90: 032313, 2014. DOI:10.1103\/PhysRevA.90.032313.","DOI":"10.1103\/PhysRevA.90.032313"},{"key":"15","doi-asserted-by":"publisher","unstructured":"M. Bavarian and P. W. Shor. Information causality, Szemer\u00e9di-Trotter and algebraic variants of CHSH. Proc. Conference on Innovations in Theoretical Computer Science, 2015. DOI:10.1145\/2688073.2688112.","DOI":"10.1145\/2688073.2688112"},{"key":"16","doi-asserted-by":"publisher","unstructured":"S.-L. Chen, C. Budroni, Y.-C. Liang, and Y.-N. Chen. Natural framework for device-independent quantification of quantum steerability, measurement incompatibility, and self-testing. Phys. Rev. Lett., 116: 240401, 2016. DOI:10.1103\/PhysRevLett.116.240401.","DOI":"10.1103\/PhysRevLett.116.240401"},{"key":"17","doi-asserted-by":"publisher","unstructured":"D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu. Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett., 88: 040404, 2002. DOI:10.1103\/PhysRevLett.88.040404.","DOI":"10.1103\/PhysRevLett.88.040404"},{"key":"18","doi-asserted-by":"publisher","unstructured":"A. Coladangelo, K. T. Goh, and V. Scarani. All pure bipartite entangled states can be self-tested. Nat. Commun., 8: 15485, 2017. DOI:10.1038\/ncomms15485.","DOI":"10.1038\/ncomms15485"},{"key":"19","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, 1969. DOI:10.1103\/PhysRevLett.23.880.","DOI":"10.1103\/PhysRevLett.23.880"},{"key":"20","doi-asserted-by":"publisher","unstructured":"R. Colbeck and A. Kent. Private randomness expansion with untrusted devices. J. Phys. A: Math. Theor., 44: 095305, 2011. DOI:10.1088\/1751-8113\/44\/9\/095305.","DOI":"10.1088\/1751-8113\/44\/9\/095305"},{"key":"21","unstructured":"R. Colbeck. Quantum and relativistic protocols for secure multi-party computation. PhD thesis, University of Cambridge, 2006."},{"key":"22","doi-asserted-by":"publisher","unstructured":"A. Coladangelo. Generalization of the Clauser-Horne-Shimony-Holt inequality self-testing maximally entangled states of any local dimension. Phys. Rev. A, 98: 052115, 2018. DOI:10.1103\/PhysRevA.98.052115.","DOI":"10.1103\/PhysRevA.98.052115"},{"key":"23","doi-asserted-by":"publisher","unstructured":"D. Cavalcanti and P. Skrzypczyk. Quantitative relations between measurement incompatibility, quantum steering, and nonlocality. Phys. Rev. A, 93: 052112, 2016. DOI:10.1103\/PhysRevA.93.052112.","DOI":"10.1103\/PhysRevA.93.052112"},{"key":"24","unstructured":"A. Coladangelo and J. Stark. Robust self-testing for linear constraint system games. 2017."},{"key":"25","unstructured":"A. Coladangelo and J. Stark. Unconditional separation of finite and infinite-dimensional quantum correlations. 2018."},{"key":"26","unstructured":"K. Dykema, V. I. Paulsen, and J. Prakash. Non-closure of the set of quantum correlations via graphs. 2017."},{"key":"27","doi-asserted-by":"publisher","unstructured":"J. I. de Vicente. Simple conditions constraining the set of quantum correlations. Phys. Rev. A, 92: 032103, 2015. DOI:10.1103\/PhysRevA.92.032103.","DOI":"10.1103\/PhysRevA.92.032103"},{"key":"28","doi-asserted-by":"publisher","unstructured":"A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47: 777, 1935. DOI:10.1103\/PhysRev.47.777.","DOI":"10.1103\/PhysRev.47.777"},{"key":"29","doi-asserted-by":"publisher","unstructured":"K. T. Goh, J. Kaniewski, E. Wolfe, T. V\u00e9rtesi, X. Wu, Y. Cai, Y.-C. Liang, and V. Scarani. Geometry of the set of quantum correlations. Phys. Rev. A, 97: 022104, 2018. DOI:10.1103\/PhysRevA.97.022104.","DOI":"10.1103\/PhysRevA.97.022104"},{"key":"30","doi-asserted-by":"publisher","unstructured":"S.-W. Ji, J. Lee, J. Lim, K. Nagata, and H.-W. Lee. Multisetting Bell inequality for qudits. Phys. Rev. A, 78: 052103, 2008. DOI:10.1103\/PhysRevA.78.052103.","DOI":"10.1103\/PhysRevA.78.052103"},{"key":"31","doi-asserted-by":"publisher","unstructured":"J. Kaniewski. Self-testing of binary observables based on commutation. Phys. Rev. A, 95: 062323, 2017. DOI:10.1103\/PhysRevA.95.062323.","DOI":"10.1103\/PhysRevA.95.062323"},{"key":"32","doi-asserted-by":"publisher","unstructured":"J. Kaniewski and S. Wehner. Device-independent two-party cryptography secure against sequential attacks. New J. Phys., 18: 055004, 2016. DOI:10.1088\/1367-2630\/18\/5\/055004.","DOI":"10.1088\/1367-2630\/18\/5\/055004"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Y.-C. Liang, C.-W. Lim, and D.-L. Deng. Reexamination of a multisetting Bell inequality for qudits. Phys. Rev. A, 80: 052116, 2009. DOI:10.1103\/PhysRevA.80.052116.","DOI":"10.1103\/PhysRevA.80.052116"},{"key":"34","doi-asserted-by":"publisher","unstructured":"J. Lim, J. Ryu, S. Yoo, C. Lee, J. Bang, and J. Lee. Genuinely high-dimensional nonlocality optimized by complementary measurements. New J. Phys., 12: 103012, 2010. DOI:10.1088\/1367-2630\/12\/10\/103012.","DOI":"10.1088\/1367-2630\/12\/10\/103012"},{"key":"35","doi-asserted-by":"publisher","unstructured":"T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. G\u00fchne. Device-independent entanglement quantification and related applications. Phys. Rev. Lett., 111: 030501, 2013. DOI:10.1103\/PhysRevLett.111.030501.","DOI":"10.1103\/PhysRevLett.111.030501"},{"key":"36","doi-asserted-by":"publisher","unstructured":"M. McKague. Self-testing graph states. Theory of Quantum Computation, Communication, and Cryptography. TQC 2011. Lecture Notes in Computer Science, 6745: 104, 2014. DOI:10.1007\/978-3-642-54429-3_7.","DOI":"10.1007\/978-3-642-54429-3_7"},{"key":"37","doi-asserted-by":"publisher","unstructured":"M. McKague and M. Mosca. Generalized self-testing and the security of the 6-state protocol. Theory of Quantum Computation, Communication, and Cryptography. TQC 2010. Lecture Notes in Computer Science, 6519: 113, 2011. DOI:10.1007\/978-3-642-18073-6_10.","DOI":"10.1007\/978-3-642-18073-6_10"},{"key":"38","doi-asserted-by":"publisher","unstructured":"C. A. Miller and Y. Shi. Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices. J. ACM, 63: 33, 2016. DOI:10.1145\/2885493.","DOI":"10.1145\/2885493"},{"key":"39","doi-asserted-by":"publisher","unstructured":"D. Mayers and A. Yao. Quantum cryptography with imperfect apparatus. Proceedings 39th Annual Symposium on Foundations of Computer Science, 1998. DOI:10.1109\/SFCS.1998.743501.","DOI":"10.1109\/SFCS.1998.743501"},{"key":"40","doi-asserted-by":"crossref","unstructured":"D. Mayers and A. Yao. Self testing quantum apparatus. Quant. Inf. Comp., 4: 273, 2004.","DOI":"10.26421\/QIC4.4-3"},{"key":"41","doi-asserted-by":"publisher","unstructured":"M. McKague, T. H. Yang, and V. Scarani. Robust self-testing of the singlet. J. Phys. A: Math. Theor., 45: 455304, 2012. DOI:10.1088\/1751-8113\/45\/45\/455304.","DOI":"10.1088\/1751-8113\/45\/45\/455304"},{"key":"42","doi-asserted-by":"publisher","unstructured":"S. Pironio, A. Ac\u00edn, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe. Random numbers certified by Bell's theorem. Nature, 464: 1021, 2010. DOI:10.1038\/nature09008.","DOI":"10.1038\/nature09008"},{"key":"43","doi-asserted-by":"publisher","unstructured":"S. Popescu and D. Rohrlich. Which states violate Bell's inequality maximally? Phys. Lett. A, 169: 411, 1992. DOI:10.1016\/0375-9601(92)90819-8.","DOI":"10.1016\/0375-9601(92)90819-8"},{"key":"44","doi-asserted-by":"publisher","unstructured":"S. Popescu and D. Rohrlich. Quantum nonlocality as an axiom. Found. Phys., 24: 379, 1994. DOI:10.1007\/BF02058098.","DOI":"10.1007\/BF02058098"},{"key":"45","unstructured":"J. Ribeiro, G. Murta, and S. Wehner. Fully general device-independence for two-party cryptography and position verification. 2016."},{"key":"46","doi-asserted-by":"publisher","unstructured":"J. Ribeiro, G. Murta, and S. Wehner. Fully device-independent conference key agreement. Phys. Rev. A, 97: 022307, 2018. DOI:10.1103\/PhysRevA.97.022307.","DOI":"10.1103\/PhysRevA.97.022307"},{"key":"47","doi-asserted-by":"publisher","unstructured":"J. Ribeiro, L. P. Thinh, J. Kaniewski, J. Helsen, and S. Wehner. Device independence for two-party cryptography and position verification with memoryless devices. Phys. Rev. A, 97: 062307, 2018. DOI:10.1103\/PhysRevA.97.062307.","DOI":"10.1103\/PhysRevA.97.062307"},{"key":"48","doi-asserted-by":"publisher","unstructured":"B. W. Reichardt, F. Unger, and U. Vazirani. Classical command of quantum systems. Nature, 496: 456, 2013. DOI:10.1038\/nature12035.","DOI":"10.1038\/nature12035"},{"key":"49","doi-asserted-by":"publisher","unstructured":"I. \u0160upi\u0107, R. Augusiak, A. Salavrakos, and A. Ac\u00edn. Self-testing protocols based on the chained Bell inequalities. New J. Phys., 18: 035013, 2016. DOI:10.1088\/1367-2630\/18\/3\/035013.","DOI":"10.1088\/1367-2630\/18\/3\/035013"},{"key":"50","doi-asserted-by":"publisher","unstructured":"A. Salavrakos, R. Augusiak, J. Tura, P. Wittek, A. Ac\u00edn, and S. Pironio. Bell inequalities tailored to maximally entangled states. Phys. Rev. Lett., 119: 040402, 2017. DOI:10.1103\/PhysRevLett.119.040402.","DOI":"10.1103\/PhysRevLett.119.040402"},{"key":"51","doi-asserted-by":"publisher","unstructured":"J. Silman, A. Chailloux, N. Aharon, I. Kerenidis, S. Pironio, and S. Massar. Fully distrustful quantum bit commitment and coin flipping. Phys. Rev. Lett., 106: 220501, 2011. DOI:10.1103\/PhysRevLett.106.220501.","DOI":"10.1103\/PhysRevLett.106.220501"},{"key":"52","doi-asserted-by":"publisher","unstructured":"I. \u0160upi\u0107, A. Coladangelo, R. Augusiak, and A. Ac\u00edn. Self-testing multipartite entangled states through projections onto two systems. New J. Phys., 20: 083041, 2018. DOI:10.1088\/1367-2630\/aad89b.","DOI":"10.1088\/1367-2630\/aad89b"},{"key":"53","doi-asserted-by":"publisher","unstructured":"W. Son, J. Lee, and M. S. Kim. Generic Bell inequalities for multipartite arbitrary dimensional systems. Phys. Rev. Lett., 96: 060406, 2006. DOI:10.1103\/PhysRevLett.96.060406.","DOI":"10.1103\/PhysRevLett.96.060406"},{"key":"54","unstructured":"W. Slofstra. The set of quantum correlations is not closed. 2017."},{"key":"55","doi-asserted-by":"publisher","unstructured":"S. J. Summers and R. F. Werner. Maximal violation of Bell's inequalities is generic in quantum field theory. Commun. Math. Phys., 110: 247, 1987. DOI:10.1007\/BF01207366.","DOI":"10.1007\/BF01207366"},{"key":"56","doi-asserted-by":"publisher","unstructured":"B. S. Tsirelson. Quantum analogues of the Bell inequalities. The case of two spatially separated domains. J. Soviet Math., 36: 557, 1987. DOI:10.1007\/BF01663472.","DOI":"10.1007\/BF01663472"},{"key":"57","unstructured":"B. S. Tsirelson. Some results and problems on quantum Bell-type inequalities. Hadronic J. Suppl., 8: 329, 1993."},{"key":"58","doi-asserted-by":"publisher","unstructured":"U. Vazirani and T. Vidick. Certifiable quantum dice: or, true random number generation secure against quantum adversaries. Proceedings 44th Annual ACM Symposium on Theory of Computing, 2012. DOI:10.1145\/2213977.2213984.","DOI":"10.1145\/2213977.2213984"},{"key":"59","doi-asserted-by":"publisher","unstructured":"U. Vazirani and T. Vidick. Fully device-independent quantum key distribution. Phys. Rev. Lett., 113: 140501, 2014. DOI:10.1103\/PhysRevLett.113.140501.","DOI":"10.1103\/PhysRevLett.113.140501"},{"key":"60","doi-asserted-by":"publisher","unstructured":"Y. Wang, X. Wu, and V. Scarani. All the self-testings of the singlet for two binary measurements. New J. Phys., 18: 025021, 2016. DOI:10.1088\/1367-2630\/18\/2\/025021.","DOI":"10.1088\/1367-2630\/18\/2\/025021"},{"key":"61","doi-asserted-by":"publisher","unstructured":"T. H. Yang and M. Navascu\u00e9s. Robust self-testing of unknown quantum systems into any entangled two-qubit states. Phys. Rev. A, 87: 050102(R), 2013. DOI:10.1103\/PhysRevA.87.050102.","DOI":"10.1103\/PhysRevA.87.050102"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-10-24-198\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,10,2]],"date-time":"2022-10-02T13:51:03Z","timestamp":1664718663000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-10-24-198\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,24]]},"references-count":62,"URL":"https:\/\/doi.org\/10.22331\/q-2019-10-24-198","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,24]]},"article-number":"198"}}