Measurement incompatibility and Schr\"odinger-EPR steering in a class of probabilistic theories
Abstract
Steering is one of the most counter intuitive non classical features of bipartite quantum system, first noticed by Schr\"odinger at the early days of quantum theory. On the other hand measurement incompatibility is another non classical feature of quantum theory, initially pointed out by N. Bohr. Recently the authors of Refs. [http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160402Phys. Rev. Lett. 113, 160402 (2014)] and [http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160403Phys. Rev. Lett. 113, 160403 (2014)] have investigated the relation between these two distinct non classical features. They have shown that a set of measurements is not jointly measurable (i.e. incompatible) if and only if they can be used for demonstrating Schr\"odinger-Einstein-Podolsky-Rosen steering. The concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.