Tripartite states Bell-nonlocality sudden death in a quantum-critical environment

We demonstrate that multipartite Bell-inequalities violations can be fully destroyed in finite time in three-qubit states under a quantum-critical environment, which is an Ising model in a transverse field. We use the Mermin–Ardehali–Belinksii–Klyshko (MABK) inequality to detect the degree of nonlocality as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of environment and the strength of transverse field on the Bell-inequality violations are given for two different initial states, namely, the W class and GHZ class states. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by the decoherence under certain conditions.