Quantum Steering and Space-Like Separation

In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables corresponding to space-like separated parties are just required to commute. The problem of determining whether these two definitions of "separation" lead to the same set of bipartite correlations is known in non-locality as Tsirelson's problem. In this article, we prove that the analog of Tsirelson's problem in steering scenarios is false. That is, there exists a steering inequality that can be violated or not depending on how we define space-like separation at the operator level.