Entanglement witness and linear entropy in an open system influenced by FG noise

We investigate the behavior of tripartite entanglement and entropy disorder in three non-interacting qubits that are first prepared in a mixture state containing Greenberger–Horne–Zeilinger (GHZ) and Werner (W) states, and then exposed to classical transmitting channels influenced by fractional Gaussian (FG) noise. To investigate the coupling of the three non-interacting qubits, single, double, and triple local channel configurations are used. We address the question of how GHZ and W states can have different capacities to protect entanglement while avoiding entropy disorder in different qubit-channel couplings. Using entanglement witness and linear entropy functions, we find that GHZ state is more resourceful when coupled with a single channel, whereas W state remains more resourceful when exposed to more than one local channel. The statistical ensemble states that are initially designed, as well as the designs of the medium to which they are exposed, have a strong influence on the initial state entanglement retention in quantum systems. Moreover, we realize that FG noise is more harmful than frequently found local noises, resulting in faster entropy disorder generation and, as a result, the destruction of tripartite quantum correlations. However, the tripartite correlations can be preserved by increasing the FG noise parameter known as the Hurst exponent.