01485nas a2200157   4500000000100000008004100001100002200042700001900064700002300083700002100106700002200127245007700149856006100226490000600287520103400293       2021                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aAleksandra Krawiec1 aRyszard Kukulski1 aMichał Oszmaniec00aMultiple-shot and unambiguous discrimination of von Neumann measurements  uhttps://quantum-journal.org/papers/q-2021-04-06-425/pdf/0 v53 a<p>We present an in-depth study of the problem of discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: unambiguous and multiple-shot discrimination. In the first scenario we give the general expressions for the optimal discrimination probabilities with and without the assistance of entanglement. In the case of multiple-shot discrimination, we focus on discrimination of measurements with the assistance of entanglement. Interestingly, we prove that in this setting all pairs of distinct von Neumann measurements can be distinguished perfectly (i.e. with the unit success probability) using only a finite number of queries. We also show that in this scenario queering the measurements \emph{in parallel} gives the optimal strategy and hence any possible adaptive methods do not offer any advantage over the parallel scheme. Finally, we show that typical pairs of Haar-random von Neumann measurements can be perfectly distinguished with only two queries.</p>