Tripartite states Bell-nonlocality sudden death in a spin environment with multisite interaction

This paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three-qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Mermin-Ardehali-Belinksii-Klyshko inequality is used 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 the environment and the strength of the three-site interaction on the Bell-inequality violations are given. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by decoherence under certain conditions for the GHZ state. The decoherence-free subspaces of our model are identified and the entanglement of quantum states is also discussed.