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://ucris.univie.ac.at/portal/en/publications/does-violation-of-a-bell-inequality-always-imply-quantum-advantage-in-a-communication-complexity-problem(69a0a5c8-ef06-4667-8175-ced4eb77fdff).html