Discrimination and certification of unknown quantum measurements

Aleksandra Krawiec1,2, Łukasz Pawela1, and Zbigniew Puchała1

1Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, Poland
2AstroCeNT, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Rektorska 4, 00-614 Warsaw, Poland

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We study the discrimination of von Neumann measurements in the scenario when we are given a reference measurement and some other measurement. The aim of the discrimination is to determine whether the other measurement is the same as the first one. We consider the cases when the reference measurement is given without the classical description and when its classical description is known. Both cases are studied in the symmetric and asymmetric discrimination setups. Moreover, we provide optimal certification schemes enabling us to certify a known quantum measurement against the unknown one.

We are given two devices. The first device is a reference device. The second device can either be the same device as the first one or not. How can we verify if the second device is the same as the first one? We study this problem when the devices are quantum measurements. We present schemes for certification when the reference device is given with its description and when that description is not known.

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