A universal scheme for robust self-testing in the prepare-and-measure scenario

Nikolai Miklin1,2 and Michał Oszmaniec3

1Institute of Theoretical Physics and Astrophysics, National Quantum Information Center, Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-306 Gdańsk, Poland
2International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdańsk, Poland
3Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland

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Abstract

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.

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[2] Armin Tavakoli, "Semi-Device-Independent Certification of Independent Quantum State and Measurement Devices", Physical Review Letters 125 15, 150503 (2020).

[3] 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).

[4] 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).

[5] 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).

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