01313nas a2200145   4500000000100000008004100001100002400042700002300066700002100089700001900110700002200129245006100151490000700212520094800219       2021                            d1 aPaulina Lewandowska1 aAleksandra Krawiec1 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aOn the optimal certification of von Neumann measurements0 v113 a<p>Certification and validation of sources producing quantum states and measurement devices are a necessary step of quantum technology. Certification of quantum measurements is entwined with quantum hypotheses testing, however, we are allowed to prepare an input state and the final measurement. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. In particular, in all the above-mentioned scenarios we characterize the optimal probability of the type II error given some fixed statistical significance. We also state the conditions when two quantum objects cannot be distinguished perfectly but still can be certified. Moreover, we show the connection between the certification of quantum channels and the notion of&nbsp;q-numerical range.</p>