QLunch: Geometry of the quantum set of correlations

Speaker: Jed Kaniewski from QMATH

Title: Geometry of the quantum set of correlations

Abstract:
Although the quantum set of correlations is the central object of study in Bell nonlocality, our understanding of its geometry is rather limited: we know little beyond the fact that it is a convex set sitting in between the local and no-signalling polytopes.

In this talk we will explore some non-trivial geometric features of the quantum set and I will give specific examples even in the simplest Bell scenario (a bipartite scenario with two inputs and two outputs). These non-trivial features are conveniently described in the language of convex geometry, which leads to a non-trivial classification of Bell functions based on the facial structure they give rise to. In the last part of the talk we will relate these geometric features to the task of self-testing.

The goal of self-testing is to deduce quantum properties of the state and/or measurements based solely on the statistics observed in a Bell experiment. All scenarios for which we can prove a self-testing statement follow a simple pattern: the maximal violation of some Bell inequality uniquely identifies the whole probability distribution, which in turn (almost uniquely) identifies the quantum system under consideration. Our results on the geometry of the quantum set show that this simple scenario is not generic and in certain cases we can only hope for weaker forms of self-testing statements.

Available at arXiv:1710.05892, based on joint work with Koon Tong Goh, Yeong- Cherng Liang, Valerio Scarani, Tamas Vertesi, Elie Wolfe, Xingyao Wu and Yu Cai.