TY - JOUR T1 - Geometry of the quantum set of correlations JF - Physical Review A Y1 - 2018 A1 - Koon Tong Goh A1 - Jedrzej Kaniewski A1 - Elie Wolfe A1 - Tamás Vértesi A1 - Xingyao Wu A1 - Yu Cai A1 - Yeong-Cherng Liang A1 - Valerio Scarani AB -

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

VL - 97 U4 - 022104 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104 CP - 2 U5 - 10.1103/PhysRevA.97.022104 ER -