Operational relevance of resource theories of quantum measurements
January 22nd, 2019 MICHAL OSZMANIEC University of Gdansk

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements (on a given Hilbert space. To this aim we prove that every resource measurement offers advantage for some quantum state discrimination task. Moreover, we give operational interpretation of robustness, which quantifies he minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resource measurement offers in a class of minimal-error state discrimination problems. Finally, we apply our results to three classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis), separable measurements (measurements whose effects are separable operators) and projective-simulable measurements. For each of these scenarios we study the maximal relative advantage that resource measurements offer for state discrimination tasks. In our analysis we will put emphasis on the asymptotic setting in which the dimension or the number of particles increase to infinity.

Seminar, January, 22, 2019, 12:30. Blue Lecture Room

Hosted by Prof. Antonio Acín