A hierarchy in the completely bounded trace norm : the more entangled, the more useful

Abstract

We show that every entangled state provides an advantage in bi- and multi-channel discrimination that singles out its degree of entanglement, quantified in terms of its Schmidt number and of the corresponding robustness measures. Namely, the more an entangled state is, the more it is useful in channel discrimination. An information-theoretic interpretation to the hierarchy is also provided. Interestingly, the hierarchy can structure the effective degrees of freedom in the interaction between a system and an environment in the dynamics of open quantum systems.