Device-independent secure correlations in sequential quantum scenarios
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AbstractDevice-independent quantum information is attracting significant attention, particularly for its applications in information security. This interest arises because the security of device-independent protocols relies solely on the observed outcomes of spatially separated measurements and the validity of quantum physics. Sequential scenarios, i.e., where measurements occur in a precise temporal order, have been proved to enhance performance of device-independent protocols in some specific cases by enabling the reuse of the same quantum state. In this work, we propose a systematic approach to designing sequential quantum protocols for device-independent security. Our method begins with a bipartite self-testing qubit protocol and transforms it into a sequential protocol by replacing one measurement with its non-projective counterpart and adding an additional user thereafter. We analytically prove that, with this systematic construction, the resulting ideal correlations are secure in the sense that they cannot be reproduced as a statistical mixture of other correlations, thereby enabling, for example, the device-independent certification of all the randomness present in the observed correlations. The general recipe we provide can be exploited for further development of new device-independent quantum schemes for security.► BibTeX data@article{Padovan2026deviceindependent, doi = {10.22331/q-2026-06-11-2131}, url = {https://doi.org/10.22331/q-2026-06-11-2131}, title = {Device-independent secure correlations in sequential quantum scenarios}, author = {Padovan, Matteo and Rezzi, Alessandro and Coccia, Lorenzo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2131}, month = jun, year = {2026} }► References [1] Valerio Scarani. ``The device-independent outlook on quantum physics (lecture notes on the power of bell's theorem)'' (2015). arXiv:1303.3081. arXiv:1303.3081 [2] Ivan Šupić and Joseph Bowles. ``Self-testing of quantum systems: a review''. Quantum 4, 337 (2020). https://doi.org/10.22331/q-2020-09-30-337 [3] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty. ``Advances in device-independent quantum key distribution''. npj Quantum Information 9 (2023). https://doi.org/10.1038/s41534-023-00684-x [4] Ignatius W. Primaatmaja, Koon Tong Goh, Ernest Y.-Z. Tan, John T.-F. Khoo, Shouvik Ghorai, and Charles C.-W. Lim. ``Security of device-independent quantum key distribution protocols: a review''. Quantum 7, 932 (2023). https://doi.org/10.22331/q-2023-03-02-932 [5] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. ``Bell nonlocality''. Rev. Mod. Phys. 86, 419–478 (2014). https://doi.org/10.1103/RevModPhys.86.419 [6] Bradley G. Christensen, Yeong-Cherng Liang, Nicolas Brunner, Nicolas Gisin, and Paul G. Kwiat. ``Exploring the limits of quantum nonlocality with entangled photons''. Phys. Rev. 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Marangon, Paolo Villoresi, and Giuseppe Vallone, "Quantum bounds and device-independent security with rank-one qubit measurements", npj Quantum Information 12 1, 29 (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-06-11 12:19:22). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-06-11 12:19:14: Could not fetch cited-by data for 10.22331/q-2026-06-11-2131 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractDevice-independent quantum information is attracting significant attention, particularly for its applications in information security. This interest arises because the security of device-independent protocols relies solely on the observed outcomes of spatially separated measurements and the validity of quantum physics. Sequential scenarios, i.e., where measurements occur in a precise temporal order, have been proved to enhance performance of device-independent protocols in some specific cases by enabling the reuse of the same quantum state. In this work, we propose a systematic approach to designing sequential quantum protocols for device-independent security. Our method begins with a bipartite self-testing qubit protocol and transforms it into a sequential protocol by replacing one measurement with its non-projective counterpart and adding an additional user thereafter. We analytically prove that, with this systematic construction, the resulting ideal correlations are secure in the sense that they cannot be reproduced as a statistical mixture of other correlations, thereby enabling, for example, the device-independent certification of all the randomness present in the observed correlations. The general recipe we provide can be exploited for further development of new device-independent quantum schemes for security.► BibTeX data@article{Padovan2026deviceindependent, doi = {10.22331/q-2026-06-11-2131}, url = {https://doi.org/10.22331/q-2026-06-11-2131}, title = {Device-independent secure correlations in sequential quantum scenarios}, author = {Padovan, Matteo and Rezzi, Alessandro and Coccia, Lorenzo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2131}, month = jun, year = {2026} }► References [1] Valerio Scarani. ``The device-independent outlook on quantum physics (lecture notes on the power of bell's theorem)'' (2015). arXiv:1303.3081. arXiv:1303.3081 [2] Ivan Šupić and Joseph Bowles. ``Self-testing of quantum systems: a review''. Quantum 4, 337 (2020). https://doi.org/10.22331/q-2020-09-30-337 [3] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty. ``Advances in device-independent quantum key distribution''. npj Quantum Information 9 (2023). https://doi.org/10.1038/s41534-023-00684-x [4] Ignatius W. Primaatmaja, Koon Tong Goh, Ernest Y.-Z. Tan, John T.-F. Khoo, Shouvik Ghorai, and Charles C.-W. Lim. ``Security of device-independent quantum key distribution protocols: a review''. Quantum 7, 932 (2023). https://doi.org/10.22331/q-2023-03-02-932 [5] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. ``Bell nonlocality''. Rev. Mod. Phys. 86, 419–478 (2014). https://doi.org/10.1103/RevModPhys.86.419 [6] Bradley G. Christensen, Yeong-Cherng Liang, Nicolas Brunner, Nicolas Gisin, and Paul G. Kwiat. ``Exploring the limits of quantum nonlocality with entangled photons''. Phys. Rev. X 5, 041052 (2015). https://doi.org/10.1103/PhysRevX.5.041052 [7] Koon Tong Goh, Jedrzej Kaniewski, Elie Wolfe, Tamás Vértesi, Xingyao Wu, Yu Cai, Yeong-Cherng Liang, and Valerio Scarani. ``Geometry of the set of quantum correlations''. Phys. Rev. A 97, 022104 (2018). https://doi.org/10.1103/PhysRevA.97.022104 [8] Antonio Acín, Serge Massar, and Stefano Pironio. ``Randomness versus nonlocality and entanglement''. Phys. Rev. Lett. 108, 100402 (2012). https://doi.org/10.1103/PhysRevLett.108.100402 [9] Carl A. Miller and Yaoyun Shi. ``Universal security for randomness expansion from the spot-checking protocol''. SIAM Journal on Computing 46, 1304–1335 (2017). https://doi.org/10.1137/15M1044333 [10] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. ``Quantum entanglement''. Rev. Mod. Phys. 81, 865–942 (2009). https://doi.org/10.1103/RevModPhys.81.865 [11] Ralph Silva, Nicolas Gisin, Yelena Guryanova, and Sandu Popescu. ``Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements''. Phys. Rev. Lett. 114, 250401 (2015). https://doi.org/10.1103/PhysRevLett.114.250401 [12] Giulio Foletto, Luca Calderaro, Armin Tavakoli, Matteo Schiavon, Francesco Picciariello, Adán Cabello, Paolo Villoresi, and Giuseppe Vallone. ``Experimental certification of sustained entanglement and nonlocality after sequential measurements''. Phys. Rev. Appl. 13, 044008 (2020). https://doi.org/10.1103/PhysRevApplied.13.044008 [13] Tinggui Zhang, Naihuan Jing, and Shao-Ming Fei. ``Sharing quantum nonlocality in star network scenarios''. Frontiers of Physics 18, 31302 (2023). https://doi.org/10.1007/s11467-022-1242-6 [14] F. J. Curchod, M. Johansson, R. Augusiak, M. J. Hoban, P. Wittek, and A. Acín. ``Unbounded randomness certification using sequences of measurements''. Phys. Rev. A 95, 020102 (2017). https://doi.org/10.1103/PhysRevA.95.020102 [15] Giulio Foletto, Matteo Padovan, Marco Avesani, Hamid Tebyanian, Paolo Villoresi, and Giuseppe Vallone. ``Experimental test of sequential weak measurements for certified quantum randomness extraction''. Phys. Rev. A 103, 062206 (2021). https://doi.org/10.1103/PhysRevA.103.062206 [16] Matteo Padovan, Giulio Foletto, Lorenzo Coccia, Marco Avesani, Paolo Villoresi, and Giuseppe Vallone. ``Secure and robust randomness with sequential quantum measurements''. npj Quantum Information 10, 94 (2024). https://doi.org/10.1038/s41534-024-00879-w [17] Joseph Bowles, Flavio Baccari, and Alexia Salavrakos. ``Bounding sets of sequential quantum correlations and device-independent randomness certification''. Quantum 4, 344 (2020). https://doi.org/10.22331/q-2020-10-19-344 [18] Yukun Wang, Xingyao Wu, and Valerio Scarani. ``All the self-testings of the singlet for two binary measurements''. New Journal of Physics 18, 025021 (2016). https://doi.org/10.1088/1367-2630/18/2/025021 [19] M McKague, T H Yang, and V Scarani. ``Robust self-testing of the singlet''. Journal of Physics A: Mathematical and Theoretical 45, 455304 (2012). https://doi.org/10.1088/1751-8113/45/45/455304 [20] T. Franz, F. Furrer, and R. F. Werner. ``Extremal quantum correlations and cryptographic security''. Phys. Rev. Lett. 106, 250502 (2011). https://doi.org/10.1103/PhysRevLett.106.250502 [21] B. S. Cirel'son. ``Quantum generalizations of bell's inequality''. Letters in Mathematical Physics 4, 93–100 (1980). https://doi.org/10.1007/BF00417500 [22] Lorenzo Coccia, Matteo Padovan, Andrea Pompermaier, Mattia Sabatini, Marco Avesani, Davide Giacomo Marangon, Paolo Villoresi, and Giuseppe Vallone. ``Quantum bounds and device-independent security with rank-one qubit measurements'' (2025). arXiv:2503.13282. https://doi.org/10.1038/s41534-025-01175-x arXiv:2503.13282 [23] O Nieto-Silleras, S Pironio, and J Silman. ``Using complete measurement statistics for optimal device-independent randomness evaluation''. New Journal of Physics 16, 013035 (2014). https://doi.org/10.1088/1367-2630/16/1/013035 [24] Jean-Daniel Bancal, Lana Sheridan, and Valerio Scarani. ``More randomness from the same data''. New Journal of Physics 16, 033011 (2014). https://doi.org/10.1088/1367-2630/16/3/033011 [25] Peter J. Brown, Sammy Ragy, and Roger Colbeck. ``A framework for quantum-secure device-independent randomness expansion''. 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Marangon, Paolo Villoresi, and Giuseppe Vallone, "Quantum bounds and device-independent security with rank-one qubit measurements", npj Quantum Information 12 1, 29 (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-06-11 12:19:22). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-06-11 12:19:14: Could not fetch cited-by data for 10.22331/q-2026-06-11-2131 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.