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Geometry of the set of quantum correlations

Koon Tong Goh, Jędrzej Kaniewski, Elie Wolfe, Tamás Vértesi, Xingyao Wu, Yu Cai, Yeong-Cherng Liang, and Valerio Scarani
Phys. Rev. A 97, 022104 – Published 7 February 2018

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.

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  • Received 14 November 2017

DOI:https://doi.org/10.1103/PhysRevA.97.022104

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Quantum Information, Science & Technology

Authors & Affiliations

Koon Tong Goh1,*, Jędrzej Kaniewski2,†, Elie Wolfe3,‡, Tamás Vértesi4, Xingyao Wu5, Yu Cai1, Yeong-Cherng Liang6,§, and Valerio Scarani1,7

  • 1Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
  • 2QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 4Institute for Nuclear Research, Hungarian Academy of Sciences, Debrecen 4001, Hungary
  • 5Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 6Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
  • 7Department of Physics, National University of Singapore, Singapore 117542, Singapore

  • *ktgoh@u.nus.edu
  • jkaniewski@math.ku.dk
  • ewolfe@perimeterinstitute.ca
  • §ycliang@mail.ncku.edu.tw

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Issue

Vol. 97, Iss. 2 — February 2018

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