Demonstration of entanglement and coherence in GHZ-like state when exposed to classical environments with power-law noise

We investigate the dynamics and protection of entanglement and coherence in three non-interacting qubits that are initially prepared as mixed entangled GHZ-like state when coupled with external classical fields. A type of Gaussian noise, namely power-law (PL) noise, controls the external local fields in three different configurations with single, double, and triple noise sources. When influenced by a single PL noise source, the GHZ-class state remains partially entangled and coherent indefinitely, in contrast to the multiple PL noise sources. However, long-term non-local correlations and coherence are still possible in the presence of multiple noise sources. In classical fluctuating environments, the PL noise restricts the entanglement sudden death and birth phenomenon, thereby preventing the conversion of free states to resource states. In addition to the noise phase, parameter optimization in local fields regulates disorders, noise effects, and memory properties. Unlike the bipartite and tripartite W-type states, the GHZ-like state has shown positive traits of preserving entanglement and coherence in the presence of PL noise.