Assemblages and steering in general probabilistic theories

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.

arXiv comment19 pages, comments welcome

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• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• A tensor norm approach to quantum compatibility
• Activation of post-quantum steering
• One-shot and asymptotic classical capacity in general physical theories