Abstract
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 resourceful measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the 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 resourceful measurement offers in a class of minimal-error state discrimination (MESD) problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separable operators). For both of these scenarios we find, in the asymptotic setting in which the dimension or the number of particles increase to infinity, the maximal relative advantage that resourceful measurements offer for state discrimination tasks.
Highlights
Resource theories [1] constitute a powerful toolbox to study physical systems in the presence of limitations resulting from experimental or operational constrains on the ability to address and manipulate physical systems
The main purpose of this work is to provide such interpretations for resource theories in which a set of free objects consists of convex subset of the set of quantum measurements (POVMs) on a relevant Hilbert space
This class contains the set of local operations assisted by classical communication (LOCC) measurements [29, 30] i.e. measurements that can be implemented via local measurements and LOCC operations. For both incoherent and separable measurements we focus on the asymptotic setting in which the dimension of the system or the number of particles involved go to infinity. In this regime we identify, for both classes of measurements, the maximal relative advantage that resourceful measurements can offer for quantum state discrimination tasks
Summary
The main purpose of this work is to provide such interpretations for resource theories in which a set of free objects consists of convex subset of the set of quantum measurements (POVMs) on a relevant Hilbert space. For both incoherent and separable measurements we focus on the asymptotic setting in which the dimension of the system or the number of particles involved go to infinity In this regime we identify, for both classes of measurements, the maximal relative advantage that resourceful measurements can offer for quantum state discrimination tasks. We believe that our results, especially previously unexplored quantitative relation between state discrimination and robustness, provide new quantitative tools to study the restricted classes of POVMs and, more generally, quantum resource theories concentrated around quantum measurements
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