Assemblages and steering in general probabilistic theories

TL;DR

This paper explores steering in general probabilistic theories, providing mathematical characterizations and extending results to infinite dimensions and multiple measurement outcomes.

Contribution

It introduces tensor cross norm and Choquet theory approaches to characterize steering in GPTs, extending quantum results to more general settings.

Findings

Steering characterized by tensor cross norm for dichotomic assemblages

Variational expression for universal steering degree

Conditions for unsteerable states analogous to quantum case

Abstract

We study steering in the framework of general probabilistic theories. We show that for dichotomic assemblages, steering can be characterized in terms of a certain tensor cross norm, which is also related to a steering degree given by steering robustness. Another contribution is the observation that steering in GPTs can be conveniently treated using Choquet theory for probability measures on the state space. In particular, we find a variational expression for universal steering degree for dichotomic assemblages and obtain conditions characterizing unsteerable states analogous to some conditions recently found for the quantum case. The setting also enables us to rather easily extend the results to infinite dimensions and arbitrary numbers of measurements with arbitrary outcomes.