Distance-based resource quantification for sets of quantum measurements

The advantage that quantum systems provide for certain information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between states have successfully been used to quantify resources like entanglement and coherence. Perhaps surprisingly, such a distance-based approach has not adopted study measurements, where other geometric quantifiers are instead. Here, we define sets measurements show they naturally induce monotones convex theories measurements. By focusing on based diamond norm, establish hierarchy measurement derive analytical bounds incompatibility any set We these tight projective mutually unbiased bases identify scenarios different attain same value when by our monotone. Our results compare allow us obtain limitations Bell-type experiments.