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Quantum correlations, in particular those, which enable to violate a Bellinequality \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 correlationsof GHZ based mixtures and Dicke states. For the former, we consider quantumcommunication complexity reduction (QCCR) scheme, and propose new Bellinequalities (BIs), which can be used in that scheme for higher persistency inthe limit of large number of particles $N$. In case of Dicke states, we showthat persistency can reach $0.482N$, significantly more than reported inprevious studies.

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