Robustness of Higher Dimensional Nonlocality against dual noise and sequential measurements

TL;DR

This paper explores the robustness of higher-dimensional quantum nonlocality against measurement and state noise, revealing a dimensional advantage in nonlocal region and demonstrating persistent sequential violations through weak measurements.

Contribution

It introduces the area of nonlocal region as a new measure and analyzes its growth with dimension, along with examining sequential violations using weak measurements in higher dimensions.

Findings

Greater enhancement in nonlocal region area with increasing dimension.

Sequential violation persists in higher dimensions with weak measurements.

Robustness to noise decreases for maximally entangled states as dimension increases.

Abstract

Robustness in the violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality is investigated from the dual perspective of noise in measurements as well as in states. To quantify it, we introduce a quantity called the area of nonlocal region which reveals a dimensional advantage. Specifically, we report that with the increase of dimension, the maximally violating states show a greater enhancement in the area of nonlocal region in comparison to the maximally entangled states and the scaling of the increment, in this case, grows faster than visibility. Moreover, we examine the robustness in the sequential violation of CGLMP inequality using weak measurements and find that even for higher dimensions, two observers showing a simultaneous violation of the CGLMP inequality as obtained for two-qubit states persists. We notice that the complementarity between information gain and disturbance by measurements is manifested by the decrease of the visibility in the first round and the increase of the same in the second round with dimensions. Furthermore, the amount of white noise that can be added to a maximally entangled state so that it gives two rounds of the violation, decreases with the dimension, while the same does not appreciably change for the maximally violating states.