Geometry of the set of quantum correlations

Koon Tong Goh, Jȩdrzej Kaniewski, Elie Wolfe, Tamás Vértesi, Xingyao Wu, Yu Cai, Yeong Cherng Liang, Valerio Scarani

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23 Citations (Scopus)

Abstract

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 a 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 counterintuitive features in the simplest nontrivial Bell scenario (two parties, two inputs, and two outputs) and illustrate them using two-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.

Original languageEnglish
Article number022104
JournalPhysical Review A
Volume97
Issue number2
DOIs
Publication statusPublished - Feb 7 2018

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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    Goh, K. T., Kaniewski, J., Wolfe, E., Vértesi, T., Wu, X., Cai, Y., Liang, Y. C., & Scarani, V. (2018). Geometry of the set of quantum correlations. Physical Review A, 97(2), [022104]. https://doi.org/10.1103/PhysRevA.97.022104