Assemblages and steering in general probabilistic theories

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 general probabilistic theories (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.

Automated summary

In this study, the concept of steering in general probabilistic theories is explored, with a focus on dichotomic assemblages. The use of a certain tensor cross norm and steering robustness to characterize steering is shown, along with the application of Choquet theory for probability measures on the state space. The study provides a variational expression for universal steering degree and conditions for unsteerable states.