Measurement incompatibility and Schr\"odinger-EPR steering in a class of probabilistic theories

TL;DR

This paper explores the relationship between measurement incompatibility and Schr"odinger-EPR steering beyond quantum mechanics, extending these concepts to general probabilistic theories and identifying their connection in a broader theoretical context.

Contribution

It generalizes the concept of measurement incompatibility and its link to steering to a wider class of probabilistic theories beyond quantum mechanics.

Findings

Measurement incompatibility can be extended to general probabilistic theories.

The connection between steering and measurement incompatibility holds in a broader class of tensor product 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. [\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160402}{Phys. Rev. Lett. {\bf 113}, 160402 (2014)}] and [\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160403}{Phys. Rev. Lett. {\bf 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.