Projective robustness for quantum channels and measurements and their operational significance
Mingfei Ye, Yu Luo, Zhihui Li, Yongming Li · Laser Physics Letters · 2022
Abstract Recently, the projective robustness of quantum states was introduced in (Regula 2022 Phys. Rev. Lett. 128 110505). This demonstrates that the projective robustness is a useful resource monotone and can comprehensively characterize the capabilities and limitations of probabilistic protocols that manipulate quantum resources deterministically. In this paper, we will extend the projective robustness to any convex resource theory of quantum channels and measurements. First, we introduce the projective robustness of quantum channels and prove that it satisfies some good properties, especially sub-multiplicativity under any free quantum process. Moreover, we show that the projective robustness of channels quantifies the maximal advantage that a given channel outperforms all free channels in the simultaneous discrimination and exclusion of a fixed-state ensemble. Second, we define the projective robustness of quantum measurements and prove that it exactly quantifies the maximal advantage that a given measurement outperforms all free measurements in the simultaneous discrimination and exclusion of two fixed-state ensembles. Finally, within a specific channel resource setting based on measurement incompatibility, we show that the projective robustness of quantum channels coincides with the projective robustness of measurement incompatibility.