{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T08:17:52Z","timestamp":1769761072684,"version":"3.49.0"},"reference-count":37,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Semi-device-independent quantum key distribution aims to achieve a balance between the highest level of security, device independence, and experimental feasibility. Semi-quantum key distribution presents an intriguing approach that seeks to minimize users&amp;apos; reliance on quantum operations while maintaining security, thus enabling the development of simplified and hardware fault-tolerant quantum protocols. In this work, we introduce a coherence-based, semi-device-independent, semi-quantum key distribution protocol built upon a noise-robust version of a coherence equality game that witnesses various types of coherence. Security is proven in the bounded quantum storage model, requiring users to implement only classical operations, specifically fixed-basis detections.<\/jats:p>","DOI":"10.22331\/q-2023-08-22-1090","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T14:34:53Z","timestamp":1692714893000},"page":"1090","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["A coherence-witnessing game and applications to semi-device-independent quantum key distribution"],"prefix":"10.22331","volume":"7","author":[{"given":"M\u00e1rio","family":"Silva","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Faleiro","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, 1049-001, Lisbon, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paulo","family":"Mateus","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, 1049-001, Lisbon, Portugal"},{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Avenida Rovisco Pais 1049-001, Lisbon, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuel Zambrini","family":"Cruzeiro","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, 1049-001, Lisbon, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. S. Sharbaf. ``Quantum cryptography: An emerging technology in network security&apos;&apos;. 2011 IEEE International Conference on Technologies for Homeland Security (HST)Pages 13\u201319 (2011).","DOI":"10.1109\/THS.2011.6107841"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Peter W. Shor. ``Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer&apos;&apos;. SIAM J. Comput., 26(5), 1484\u20131509 (1997).","DOI":"10.1137\/S0097539795293172"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Charles H. Bennett and Gilles Brassard. ``Quantum cryptography: Public key distribution and coin tossing&apos;&apos;. Theoretical Computer Science 560, 7\u201311 (2014).","DOI":"10.1016\/j.tcs.2014.05.025"},{"key":"3","unstructured":"Dominic Mayers and Andrew Yao. ``Quantum cryptography with imperfect apparatus&apos;&apos;. Proceedings of the 39th Annual Symposium on Foundations of Computer Science (1998)."},{"key":"4","doi-asserted-by":"crossref","unstructured":"Dominic Mayers and Andrew Yao. ``Self testing quantum apparatus&apos;&apos;. Quantum Info. Comput. 4, 273\u2013286 (2004).","DOI":"10.26421\/QIC4.4-3"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Umesh Vazirani and Thomas Vidick. ``Fully device-independent quantum key distribution&apos;&apos;. Physical Review Letters 113 (2014).","DOI":"10.1103\/physrevlett.113.140501"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Rotem Arnon-Friedman, Fr\u00e9d\u00e9ric Dupuis, Omar Fawzi, Renato Renner, and Thomas Vidick. ``Practical device-independent quantum cryptography via entropy accumulation&apos;&apos;. Nature Communications 9, 459 (2018).","DOI":"10.1038\/s41467-017-02307-4"},{"key":"7","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 et al. ``Random numbers certified by bell\u2019s theorem&apos;&apos;. Nature 464, 1021\u20131024 (2010).","DOI":"10.1038\/nature09008"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Antonio Ac\u00edn, Serge Massar, and Stefano Pironio. ``Randomness versus nonlocality and entanglement&apos;&apos;. Phys. Rev. Lett. 108, 100402 (2012).","DOI":"10.1103\/PhysRevLett.108.100402"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Nati Aharon, Andr\u00e9 Chailloux, Iordanis Kerenidis, Serge Massar, Stefano Pironio, and Jonathan Silman. ``Weak coin flipping in a device-independent setting&apos;&apos;. In Revised Selected Papers of the 6th Conference on Theory of Quantum Computation, Communication, and Cryptography - Volume 6745, pg.1\u201312. TQC 2011 (2011).","DOI":"10.1007\/978-3-642-54429-3_1"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Ricardo Faleiro and Manuel Goul\u00e3o. ``Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game&apos;&apos;. Phys. Rev. A 103, 022430 (2021).","DOI":"10.1103\/PhysRevA.103.022430"},{"key":"11","doi-asserted-by":"publisher","unstructured":"D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E. Y.-Z. Tan, P. Sekatski, R. L. Urbanke, R. Renner, N. Sangouard, and J.-D. Bancal. ``Experimental quantum key distribution certified by bell&apos;s theorem&apos;&apos;. Nature 607, 682\u2013686 (2022).","DOI":"10.1038\/s41586-022-04941-5"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Wei Zhang, Tim van Leent, Kai Redeker, Robert Garthoff, Ren\u00e9 Schwonnek, Florian Fertig, Sebastian Eppelt, Wenjamin Rosenfeld, Valerio Scarani, Charles C.-W. Lim, and Harald Weinfurter. ``A device-independent quantum key distribution system for distant users&apos;&apos;. Nature 607, 687\u2013691 (2022).","DOI":"10.1038\/s41586-022-04891-y"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Wen-Zhao Liu, Yu-Zhe Zhang, Yi-Zheng Zhen, Ming-Han Li, Yang Liu, Jingyun Fan, Feihu Xu, Qiang Zhang, and Jian-Wei Pan. ``Toward a photonic demonstration of device-independent quantum key distribution&apos;&apos;. Phys. Rev. Lett. 129, 050502 (2022).","DOI":"10.1103\/PhysRevLett.129.050502"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Marcin Paw\u0142owski and Nicolas Brunner. ``Semi-device-independent security of one-way quantum key distribution&apos;&apos;. Phys. Rev. A 84, 010302 (2011).","DOI":"10.1103\/PhysRevA.84.010302"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Anubhav Chaturvedi, Maharshi Ray, Ryszard Veynar, and Marcin Paw\u0142owski. ``On the security of semi-device-independent QKD protocols&apos;&apos;. Quantum Information Processing 17, 131 (2018).","DOI":"10.1007\/s11128-018-1892-z"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Armin Tavakoli, J\u0119drzej Kaniewski, Tam\u00e1s V\u00e9rtesi, Denis Rosset, and Nicolas Brunner. ``Self-testing quantum states and measurements in the prepare-and-measure scenario&apos;&apos;. Phys. Rev. A 98, 062307 (2018).","DOI":"10.1103\/PhysRevA.98.062307"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Armin Tavakoli. ``Semi-device-independent certification of independent quantum state and measurement devices&apos;&apos;. Phys. Rev. Lett. 125, 150503 (2020).","DOI":"10.1103\/PhysRevLett.125.150503"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Thomas Van Himbeeck, Erik Woodhead, Nicolas J. Cerf, Ra\u00fal Garc\u00eda-Patr\u00f3n, and Stefano Pironio. ``Semi-device-independent framework based on natural physical assumptions&apos;&apos;. Quantum 1, 33 (2017).","DOI":"10.22331\/q-2017-11-18-33"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Erik Woodhead, and Stefano Pironio. ``Informationally restricted correlations: a general framework for classical and quantum systems&apos;&apos;. Quantum 6, 620 (2022).","DOI":"10.22331\/q-2022-01-05-620"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Erik Woodhead, and Stefano Pironio. ``Informationally restricted correlations: a general framework for classical and quantum systems&apos;&apos;. Quantum 6, 620 (2022).","DOI":"10.22331\/q-2022-01-05-620"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Weixu Shi, Yu Cai, Jonatan Bohr Brask, Hugo Zbinden, and Nicolas Brunner. ``Semi-device-independent characterization of quantum measurements under a minimum overlap assumption&apos;&apos;. Phys. Rev. A 100, 042108 (2019).","DOI":"10.1103\/PhysRevA.100.042108"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Hasan Iqbal and Walter O. Krawec. ``Semi-quantum cryptography&apos;&apos;. Quantum Information Processing 19, 97 (2020).","DOI":"10.1007\/s11128-020-2595-9"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Michel Boyer, Ran Gelles, Dan Kenigsberg, and Tal Mor. ``Semiquantum key distribution&apos;&apos;. Phys. Rev. A 79, 032341 (2009).","DOI":"10.1103\/PhysRevA.79.032341"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Francesco Massa, Preeti Yadav, Amir Moqanaki, Walter O. Krawec, Paulo Mateus, Nikola Paunkovi\u0107, Andr\u00e9 Souto, and Philip Walther. ``Experimental Semi-quantum Key Distribution With Classical Users&apos;&apos;. Quantum 6, 819 (2022).","DOI":"10.22331\/q-2022-09-22-819"},{"key":"25","doi-asserted-by":"publisher","unstructured":"Flavio Del Santo and Borivoje Daki\u0107. ``Coherence equality and communication in a quantum superposition&apos;&apos;. Physical Review Letters 124 (2020).","DOI":"10.1103\/physrevlett.124.190501"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Lieven Vandenberghe and Stephen Boyd. ``Semidefinite programming&apos;&apos;. SIAM Rev. 38, 49\u201395 (1996).","DOI":"10.1137\/1038003"},{"key":"27","doi-asserted-by":"publisher","unstructured":"K\u00e1roly F. P\u00e1l and Tam\u00e1s V\u00e9rtesi. ``Efficiency of higher-dimensional hilbert spaces for the violation of bell inequalities&apos;&apos;. Phys. Rev. A 77, 042105 (2008).","DOI":"10.1103\/PhysRevA.77.042105"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Matthew McKague, Michele Mosca, and Nicolas Gisin. ``Simulating quantum systems using real hilbert spaces&apos;&apos;. Phys. Rev. Lett. 102, 020505 (2009).","DOI":"10.1103\/PhysRevLett.102.020505"},{"key":"29","doi-asserted-by":"publisher","unstructured":"K. C. Toh, M. J. Todd, and R. H. T\u00fct\u00fcnc\u00fc. ``Sdpt3 \u2014 a matlab software package for semidefinite programming, version 1.3&apos;&apos;. Optimization Methods and Software 11, 545\u2013581 (1999).","DOI":"10.1080\/10556789908805762"},{"key":"30","unstructured":"Reinhard F. Werner and Michael M. Wolf. ``Bell inequalities and entanglement&apos;&apos; (2001). arXiv:quant-ph\/0107093."},{"key":"31","doi-asserted-by":"publisher","unstructured":"J. Lofberg. ``Yalmip : a toolbox for modeling and optimization in matlab&apos;&apos;. In 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508). Pages 284\u2013289. (2004).","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"32","doi-asserted-by":"publisher","unstructured":"S\u00e9bastien Designolle, Roope Uola, Kimmo Luoma, and Nicolas Brunner. ``Set coherence: Basis-independent quantification of quantum coherence&apos;&apos;. Phys. Rev. Lett. 126, 220404 (2021).","DOI":"10.1103\/PhysRevLett.126.220404"},{"key":"33","unstructured":"Rafael Wagner, Rui Soares Barbosa, and Ernesto F. Galv\u00e3o. ``Inequalities witnessing coherence, nonlocality, and contextuality&apos;&apos; (2023). arXiv:2209.02670."},{"key":"34","doi-asserted-by":"publisher","unstructured":"Kazuoki Azuma. ``Weighted sums of certain dependent random variables&apos;&apos;. Tohoku Math. J. (2) 19, 357\u2013367 (1967).","DOI":"10.2748\/tmj\/1178243286"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Renato Renner. ``Security of quantum key distribution&apos;&apos;. International Journal of Quantum Information 6, 1\u2013127 (2008).","DOI":"10.1142\/S0219749908003256"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Robert Konig, Renato Renner, and Christian Schaffner. ``The operational meaning of min- and max-entropy&apos;&apos;. IEEE Transactions on Information Theory 55, 4337\u20134347 (2009).","DOI":"10.1109\/tit.2009.2025545"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-08-22-1090\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T14:34:57Z","timestamp":1692714897000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-08-22-1090\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,22]]},"references-count":37,"URL":"https:\/\/doi.org\/10.22331\/q-2023-08-22-1090","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,22]]},"article-number":"1090"}}