One-to-One Mapping between Steering and Joint Measurability Problems

“…First, it shows that the non-classicality of quantum measurements is not sufficient in general to generate nonclassical correlations, in the sense of violating a Bell inequality. This is in contrast with recent results [17][18][19] proving a one-to-one relation between non joint measurability and quantum steering, a weaker notion of quantum nonlocality. Second, our work shows that the direct connection between the quantum violation of the CHSH inequality (the simplest Bell inequality) and non joint measurability of two binary POVMs proven in Ref.…”

“…This allows to recast bounds derived for the former probability into inequalities holding for the latter quantifier of incompatibility. Such a result parallels the correspondence between steering inequalities and joint measurability criteria explored in [23].…”

“…Here we give an operational interpretation of measurement incompatibility in terms of quantum state discrimination: we show that a set of measurements is incompatible if and only if they provide an advantage over compatible ones in a quantum state discrimination (QSD) task with multiple ensembles of states. Moreover, we also show that the advantage of an optimally chosen QSD task is quantified exactly by the robustness of incompatibility of the set, a previously proposed quantifier of measurement incompatibility [6]. This result fits within a number of results recently obtained which have linked robustness-based quantifiers with advantages in suitably chosen discrimination games [7][8][9][10][11]…”