Tripartite Entanglement for Three-Qubit System in the Generalized Coleman-Hepp Model

Based on the solvable dynamical model for quantum measurement process, we consider three uncoupled particles interacting with their local one-dimensional (1D) spin arrays. Here the 1D spin arrays can be regarded as the local phase decoherence environments for the particles. To demonstrate the dynamics of quantum entanglement among three particles in measuring process, the tripartite negativity is introduced. Our study indicates that the tripartite negativity is determined jointly by the initial states and the dephasing factors for four kinds of initial states, including GHZ-type states, W-type states, Weiner-GHZ states, and Weiner-W states. We find the particle-spin array interaction can destroy the tripartite negativity, and the tripartite negativity is the same for the family of entangled GHZ states or the family of entangled W states. Furthermore, there exists the sudden death of tripartite negativity when the initial states are Weiner-GHZ states or Weiner-W states.