Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures: studying the limits of monogamy

TL;DR

This paper investigates the robustness of Bell correlations in GHZ-based mixtures and Dicke states, proposing new Bell inequalities and demonstrating high persistency levels, which are crucial for quantum communication and understanding quantum correlations.

Contribution

It introduces new Bell inequalities for GHZ-based mixtures and quantifies the high persistency of Bell correlations in Dicke states, advancing understanding of quantum correlation robustness.

Findings

New Bell inequalities enable higher persistency in GHZ-based schemes.

Dicke states exhibit persistency up to 0.482N, surpassing previous results.

Results improve the understanding of quantum correlation robustness against noise.

Abstract

Quantum correlations, in particular those, which enable to violate a Bell inequality \cite{BELL}, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles $N$. In case of Dicke states, we show that persistency can reach $0.482N$, significantly more than reported in previous studies.