Survey on the Bell nonlocality of a pair of entangled qudits

Alejandro Fonseca , Anna de Rosier , Tamás Vértesi , Wiesław Laskowski , Fernando Parisio

Abstract

The question of how Bell nonlocality behaves in bipartite systems of higher dimensions is addressed. By employing the probability of violation of local realism under random measurements as the figure of merit, we investigate the nonlocality of entangled qudits with dimensions ranging from d=2 up to d=10. We proceed in two complementary directions. First, we study the specific Bell scenario defined by the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality. Second, we consider the nonlocality of the same states under a more general perspective by directly addressing the space of joint probabilities (computing the frequencies of behaviours outside the local polytope). In both approaches we find that the nonlocality decreases as the dimension d grows, but in quite distinct ways. While the drop in the probability of violation is exponential in the CGLMP scenario, it presents, at most, a linear decay in the space of behaviors. Furthermore, in the latter approach the states that produce maximal numeric violations in the CGLMP inequality present low probabilities of violation in comparison to maximally entangled states, so no anomaly is observed. Finally, the nonlocality of states with nonmaximal Schmidt rank is investigated.
Author Alejandro Fonseca
Alejandro Fonseca,,
-
, Anna de Rosier (FMPI)
Anna de Rosier ,,
- Faculty of Mathematics, Physics and Informatics
, Tamás Vértesi
Tamás Vértesi,,
-
, Wiesław Laskowski (FMPI / ITPA)
Wiesław Laskowski,,
- Institute of Theoretical Physics and Astrophysics
, Fernando Parisio
Fernando Parisio,,
-
Journal seriesPhysical Review A, ISSN 1050-2947, (A 35 pkt)
Issue year2018
Vol98
No4
Pages1-8
Publication size in sheets0.5
DOIDOI:10.1103/PhysRevA.98.042105
URL https://journals.aps.org/pra/pdf/10.1103/PhysRevA.98.042105
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 24-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 24-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.925 (2) - 2016=2.716 (5)
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