We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert space. To this aim, we propose a universal and intuitive scheme based on establishing perfect correlations between target states and suitably-chosen projective measurements. The method works in all finite dimensions and allows for robust certification of the overlaps between arbitrary preparation states and between the corresponding measurement operators. Finally, we prove that for qubits, our technique can be used to robustly self-test arbitrary configurations of pure quantum states and projective measurements. These results pave the way towards the practical application of the prepare-and-measure paradigm to certification of quantum devices.
 F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. P. Harrigan, M. J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S. Humble, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. V. Klimov, S. Knysh, A. Korotkov, F. Kostritsa, D. Land huis, M. Lindmark, E. Lucero, D. Lyakh, S. Mandrà, J. R. McClean, M. McEwen, A. Megrant, X. Mi, K. Michielsen, M. Mohseni, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Y. Niu, E. Ostby, A. Petukhov, J. C. Platt, C. Quintana, E. G. Rieffel, P. Roushan, N. C. Rubin, D. Sank, K. J. Satzinger, V. Smelyanskiy, K. J. Sung, M. D. Trevithick, A. Vainsencher, B. Villalonga, T. White, Z. J. Yao, P. Yeh, A. Zalcman, H. Neven, and J. M. Martinis, Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019).
 V. Dunjko and H. J. Briegel, Machine learning & artificial intelligence in the quantum domain: a review of recent progress, Reports on Progress in Physics 81, 074001 (2018).
 J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Quantum certification and benchmarking, Nature Reviews Physics 2, 382 (2020).
 J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika 1, 195 (1964).
 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, Physical Review Letters 116, 240401 (2016).
 J. Bowles, I. Šupić, D. Cavalcanti, and A. Acín, Device-independent entanglement certification of all entangled states, Physical Review Letters 121, 180503 (2018).
 J. Ahrens, P. Badziąg, M. Pawłowski, M. Żukowski, and M. Bourennane, Experimental tests of classical and quantum dimensionality, Physical Review Letters 112, 140401 (2014).
 J. B. Brask, A. Martin, W. Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Megahertz-rate semi-device-independent quantum random number generators based on unambiguous state discrimination, Physical Review Applied 7, 054018 (2017).
 E. A. Aguilar, M. Farkas, D. Martínez, M. Alvarado, J. Cariñe, G. B. Xavier, J. F. Barra, G. Cañas, M. Pawłowski, and G. Lima, Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses, Physical Review Letters 120, 230503 (2018).
 H. Anwer, S. Muhammad, W. Cherifi, N. Miklin, A. Tavakoli, and M. Bourennane, Experimental characterization of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes, Physical Review Letters 125, 080403 (2020).
 T. Van Himbeeck, E. Woodhead, N. J. Cerf, R. García-Patrón, and S. Pironio, Semi-device-independent framework based on natural physical assumptions, Quantum 1, 33 (2017).
 R. Chaves, J. B. Brask, and N. Brunner, Device-independent tests of entropy, Physical Review Letters 115, 110501 (2015).
 T. Fritz, Quantum correlations in the temporal Clauser–Horne–Shimony–Holt (CHSH) scenario, New Journal of Physics 12, 083055 (2010).
 A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Self-testing quantum states and measurements in the prepare-and-measure scenario, Physical Review A 98, 062307 (2018).
 P. Mironowicz and M. Pawłowski, Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements, Physical Review A 100, 030301 (2019).
 A. Tavakoli, M. Smania, T. Vértesi, N. Brunner, and M. Bourennane, Self-testing non-projective quantum measurements, Science Advances 6, eaaw6664 (2020).
 A. Tavakoli, D. Rosset, and M.-O. Renou, Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrization, Physical Review Letters 122, 070501 (2019).
 R. Blume-Kohout, J. K. Gamble, E. Nielsen, K. Rudinger, J. Mizrahi, K. Fortier, and P. Maunz, Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography, Nature Communications 8, 1 (2017).
 E. Woodhead, C. C. W. Lim, and S. Pironio, Semi-device-independent QKD based on BB84 and a CHSH-type estimation, In Theory of Quantum Computation, Communication, and Cryptography, vol 7582, pages 107–115, Springer, Berlin, Heidelberg (2013).
 M. Navascués and S. Popescu, How energy conservation limits our measurements, Physical Review Letters 112, 140502 (2014).
 J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric informationally complete quantum measurements, Journal of Mathematical Physics 45, 2171 (2004).
 M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press, USA, 10th edition (2011).
 E. Arias-Castro, A. Javanmard, and B. Pelletier, Perturbation bounds for Procrustes, classical scaling, and trilateration, with applications to manifold learning, Journal of Machine Learning Research 21, 15 (2020).
 G. M. D'Ariano, P. L. Presti, and P. Perinotti, Classical randomness in quantum measurements, Journal of Physics A: Mathematical and General 38, 5979 (2005).
 R. Takagi and B. Regula, General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks, Physical Review X 9, 031053 (2019).
 R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. Gühne, Quantifying quantum resources with conic programming, Physical Review Letters 122, 130404 (2019).
 A. Tavakoli, Semi-device-independent certification of independent quantum state and measurement devices, Physical Review Letters 125, 150503 (2020).
 J. R. Hurley and R. B. Cattell, The Procrustes program: Producing direct rotation to test a hypothesized factor structure, Behavioral Science 7, 258 (1962).
 Armin Tavakoli, "Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments", Physical Review Letters 126 21, 210503 (2021).
 Qing Zhou, Xin-Yu Xu, Shuai Zhao, Yi-Zheng Zhen, Li Li, Nai-Le Liu, and Kai Chen, "Robust self-testing of multipartite Greenberger-Horne-Zeilinger-state measurements in quantum networks", Physical Review A 106 4, 042608 (2022).
 Xing-Xiang Peng, Wen-Hao Zhang, Peng Yin, Gong-Chu Li, Lei Chen, Geng Chen, Chuan-Feng Li, and Guang-Can Guo, "Trusted quantum remote sensing based on self-testing of entangled states", Physical Review A 105 3, 032615 (2022).
 Carlos Vieira, Carlos de Gois, Lucas Pollyceno, and Rafael Rabelo, "Interplays between classical and quantum entanglement-assisted communication scenarios", New Journal of Physics 25 11, 113004 (2023).
 Shubhayan Sarkar, Debashis Saha, and Remigiusz Augusiak, "Certification of incompatible measurements using quantum steering", Physical Review A 106 4, L040402 (2022).
 Armin Tavakoli, "Semi-Device-Independent Certification of Independent Quantum State and Measurement Devices", Physical Review Letters 125 15, 150503 (2020).
 George Moreno, Ranieri Nery, Carlos de Gois, Rafael Rabelo, and Rafael Chaves, "Semi-device-independent certification of entanglement in superdense coding", Physical Review A 103 2, 022426 (2021).
 Carlos de Gois, George Moreno, Ranieri Nery, Samuraí Brito, Rafael Chaves, and Rafael Rabelo, "General Method for Classicality Certification in the Prepare and Measure Scenario", PRX Quantum 2 3, 030311 (2021).
 Shihui Wei, Fenzhuo Guo, Fei Gao, and Qiaoyan Wen, "Certification of three black boxes with unsharp measurements using 3 → 1 sequential quantum random access codes", New Journal of Physics 23 5, 053014 (2021).
 Boaz Hilman, Jan Muhr, Susan E. Trumbore, Norbert Kunert, Mariah S. Carbone, Päivi Yuval, S. Joseph Wright, Gerardo Moreno, Oscar Pérez-Priego, Mirco Migliavacca, Arnaud Carrara, José M. Grünzweig, Yagil Osem, Tal Weiner, and Alon Angert, "Comparison of CO<SUB>2</SUB> and O<SUB>2</SUB> fluxes demonstrate retention of respired CO<SUB>2</SUB> in tree stems from a range of tree species", Biogeosciences 16 1, 177 (2019).
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