Full separability of four-qubit GHZ and W mixed states in white noise

Entanglement witnesses are fundamental tools for detecting entanglement. We prove the necessary and sufficient conditions via two entanglement witnesses for the full separability of system of the four-qubit GHZ and W mixed states in white noise in some parameter regions. The witnesses lead to the necessary conditions. For the sufficiency of the system, we generate three types of optimal product states. Then we show how to combine optimal product states to construct the four-qubit fully separable GHZ and W mixed states in white noise.

Automated summary

In this article, we provide necessary and sufficient conditions for the full separability of four-qubit GHZ and W mixed states using entanglement witnesses. We also present a method for constructing optimal product states.