Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?

Author(s)
Armin Tavakoli, Marek Żukowski, Časlav Brukner
Abstract

Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, [Brukner et. al.. Phys Rev. Lett. 89. 197901 (2002)]; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the [3:122 Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs

Organisation(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
Université de Genève, University of Gdańsk, Österreichische Akademie der Wissenschaften (ÖAW)
Journal
Quantum
Volume
4
No. of pages
11
ISSN
2521-327X
DOI
https://doi.org/10.22331/q-2020-09-07-316
Publication date
09-2020
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics
ASJC Scopus subject areas
Atomic and Molecular Physics, and Optics, Physics and Astronomy (miscellaneous)
Portal url
https://ucrisportal.univie.ac.at/en/publications/69a0a5c8-ef06-4667-8175-ced4eb77fdff