Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states

TL;DR

This paper provides an operational interpretation of the weight of resource in convex quantum resource theories, linking it to exclusion advantages and information-theoretic quantities, and applies it to entanglement quantification.

Contribution

It introduces a resource quantifier called weight of resource with an operational meaning and connects it to exclusion tasks and information measures in convex quantum resource theories.

Findings

The weight of resource captures the advantage in exclusion tasks.

A connection between weight of resource and exclusion-type information is established.

The results apply to entanglement, interpreting the Lewenstein-Sanpera decomposition operationally.

Abstract

We introduce the resource quantifier of weight of resource for convex quantum resource theories of states with arbitrary resources. We show that it captures the advantage that a resourceful state offers over all possible free states, in the operational task of exclusion of subchannels. Furthermore, we introduce information-theoretic quantities related to exclusion and find a connection between the weight of resource of a state, and the exclusion-type information of ensembles it can generate. These results provide support to a recent conjecture made in the context of convex quantum resource theories of measurements, about the existence of a weight-exclusion correspondence whenever there is a robustness-discrimination one. The results found in this article apply to the resource theory of entanglement, in which the weight of resource is known as the best-separable approximation or Lewenstein-Sanpera decomposition, introduced in 1998. Consequently, the results found here provide an operational interpretation to this 21 year-old entanglement quantifier.