### 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.

Original language | English |
---|---|

Article number | 042105 |

Journal | Physical Review A |

Volume | 98 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 3 2018 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*98*(4), [042105]. https://doi.org/10.1103/PhysRevA.98.042105

**Survey on the Bell nonlocality of a pair of entangled qudits.** / Fonseca, Alejandro; De Rosier, Anna; Vértesi, T.; Laskowski, Wiesław; Parisio, Fernando.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 98, no. 4, 042105. https://doi.org/10.1103/PhysRevA.98.042105

}

TY - JOUR

T1 - Survey on the Bell nonlocality of a pair of entangled qudits

AU - Fonseca, Alejandro

AU - De Rosier, Anna

AU - Vértesi, T.

AU - Laskowski, Wiesław

AU - Parisio, Fernando

PY - 2018/10/3

Y1 - 2018/10/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85054513078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054513078&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.042105

DO - 10.1103/PhysRevA.98.042105

M3 - Article

AN - SCOPUS:85054513078

VL - 98

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 042105

ER -