Tripartite Separability of Four-Qubit W and Dicke Mixed State in Noise Environment

Quantum entanglement is one of the most important resources in quantum information. A certain degree of white noise will make the entangled state separable, so finding the minimal white noise tolerance of a specific state is important. Based on a detailed study of the tripartite separability of a four-qubit W state mixed with a Dicke state and white noise, we obtain the necessary and (or) sufficient conditions either numerically or analytically. In particular, we give the analytical formula at W state side, our results show that the sufficient condition of tripartite separability agrees with the necessary condition well.