Steering, incompatibility, and Bell-inequality violations in a class of probabilistic theories

Paul Busch; Neil Stevens

doi:10.1103/PhysRevA.89.022123

Steering, incompatibility, and Bell-inequality violations in a class of probabilistic theories

Paul Busch, Neil Stevens

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that connections between a degree of incompatibility of pairs of observables and the strength of violations of Bell’s inequality found in recent investigations can be extended to a general class of probabilistic physical models. It turns out that the property of universal uniform steering is sufficient for the saturation of a generalized Tsirelson bound, corresponding to maximal violations of Bell’s inequality. It is also found that a limited form of steering is still available and sufficient for such saturation in some state spaces where universal uniform steering is not given. The techniques developed here are applied to the class of regular polygon state spaces, giving a strengthening of known results. However, we also find indications that the link between incompatibility and Bell violation may be more complex than originally envisaged.

Original language	English
Article number	022123
Journal	Physical Review A
Volume	89
Issue number	2
Early online date	24 Feb 2014
DOIs	https://doi.org/10.1103/PhysRevA.89.022123
Publication status	Published - 24 Feb 2014

Keywords

quantum mechanics
nonlocality

Access to Document

10.1103/PhysRevA.89.022123

https://arxiv.org/abs/1311.1462

Cite this

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abstract = "We show that connections between a degree of incompatibility of pairs of observables and the strength of violations of Bell{\textquoteright}s inequality found in recent investigations can be extended to a general class of probabilistic physical models. It turns out that the property of universal uniform steering is sufficient for the saturation of a generalized Tsirelson bound, corresponding to maximal violations of Bell{\textquoteright}s inequality. It is also found that a limited form of steering is still available and sufficient for such saturation in some state spaces where universal uniform steering is not given. The techniques developed here are applied to the class of regular polygon state spaces, giving a strengthening of known results. However, we also find indications that the link between incompatibility and Bell violation may be more complex than originally envisaged.",

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