Activation of hidden nonlocality using local filtering operations based on CGLMP inequality

TL;DR

This paper demonstrates hidden nonlocality activation in mixed entangled states across arbitrary dimensions using local filtering and CGLMP inequality violations, revealing nonlocality for broader parameter ranges than previously known.

Contribution

It introduces a method to activate hidden nonlocality in mixed states of arbitrary dimension via local filtering and CGLMP inequality, expanding the understanding of nonlocality activation.

Findings

Hidden nonlocality can be revealed for mixed states in any dimension using local filtering.

For dimensions d ≥ 8, hidden nonlocality is revealed for all mixing parameters.

Activation of nonlocality is demonstrated with maximally entangled and maximally CGLMP-violating states.

Abstract

Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in $d \geq 5$. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary $d$-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for $d \geq 8$, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation.