Complete classification of steerability under local filters and its relation with measurement incompatibility

The study of quantum steering has both foundational and practical interest. Here, the authors show that transformability of a steerable resource into another via local filtering at the trusted party is determined by whether they have the same steering equivalent observables (SEO). Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

Automated summary

The study explores the importance of quantum steering in both theoretical foundations and practical applications. The researchers propose a condition for transforming a steerable resource into another via local filtering, based on the concept of steering equivalent observables (SEO). They provide an efficient method for computing the maximum extractable steerability via local filters and demonstrate its equivalence to the incompatibility of the SEO. Additionally, they investigate the optimal performance of transformation protocols in the single-shot scenario.