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

TL;DR

This paper provides a complete characterization of when quantum steering can be transformed via local filters, linking steerability to measurement incompatibility, and offers methods to compute and optimize these transformations.

Contribution

It introduces a necessary and sufficient condition for steerability transformation under local filters and connects it with measurement incompatibility through the SEO framework.

Findings

Characterizes steerability transformation with local filters.

Shows equivalence between maximal steerability and measurement incompatibility.

Provides methods for optimal steering distillation and dilution.

Abstract

Quantum steering is the 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 one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability 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.