Robust certification of arbitrary outcome quantum measurements from temporal correlations

Debarshi Das1,2, Ananda G. Maity1, Debashis Saha1, and A. S. Majumdar1

1S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
2Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, UK

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Certification of quantum devices received from unknown providers is a primary requirement before utilizing the devices for any information processing task. Here, we establish a protocol for certification of a particular set of $d$-outcome quantum measurements (with $d$ being arbitrary) in a setup comprising of a preparation followed by two measurements in sequence. We propose a set of temporal inequalities pertaining to different $d$ involving correlation functions corresponding to successive measurement outcomes, that are not satisfied by quantum devices. Using quantum violations of these inequalities, we certify specific $d$-outcome quantum measurements under some minimal assumptions which can be met in an experiment efficiently. Our certification protocol neither requires entanglement, nor any prior knowledge about the dimension of the system under consideration. We further show that our protocol is robust against practical non-ideal realizations. Finally, as an offshoot of our protocol, we present a scheme for secure certification of genuine quantum randomness.

With emerging quantum technology, it is important to design experiments which can test whether the quantum devices received from unknown providers function properly. Certification protocols are designed for this purpose. Since quantum measurements are one of the key resources of modern quantum technologies and play a crucial role in revealing unique quantum phenomena, we aim to design certification protocols of quantum measurements having arbitrary number of outcomes with the desiderata of efficiency and less resource consumption. In particular, we propose a method to certify a particular set of quantum measurements having fundamental significance as well as information theoretic applications using temporal quantum correlations. Our proposed method works under some minimal assumptions which can be met in an experiment efficiently. However, our method requires neither entanglement between space-like separated systems, nor any prior knowledge about the dimension of the system under consideration. We also demonstrate the efficacy of our protocol in practical non-ideal situations. Although we propose certification protocol of some specific quantum measurements with arbitrary number of outcomes, the method presented by us is quite general and can be immediately applied in different contexts to certify a wide range of quantum measurements employing temporal quantum correlations. Finally, we present genuine quantum randomness certification as an application of our proposed protocol.

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[2] Miguel Navascués, Károly F. Pál, Tamás Vértesi, and Mateus Araújo, "Self-Testing in Prepare-and-Measure Scenarios and a Robust Version of Wigner’s Theorem", Physical Review Letters 131 25, 250802 (2023).

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