Incompatibility in restricted operational theories: connecting contextuality and steering

TL;DR

This paper explores the relationship between steering and contextuality within general probabilistic theories, revealing their equivalence under certain conditions and highlighting the role of incompatibility in restricted theories.

Contribution

It establishes a novel connection between steering and contextuality, demonstrating their equivalence for specific bipartite states in restricted theories, and investigates incompatibility's role.

Findings

Steerability is equivalent to the non-existence of a noncontextual hidden variable model in certain theories.

Incompatibility in restricted theories underpins the connection between steering and contextuality.

The work broadens understanding of foundational quantum phenomena in generalized probabilistic frameworks.

Abstract

We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories, which we also investigate.