Effects of intrinsic decoherence in multipartite system subjected to Kerr effect and parametric amplification with quantum correlations and estimation

We investigate the interplay between quantum correlations, quantified by global quantum discord (GQD), and quantum Fisher information (QFI) within a multipartite two-level system interacting with a single-mode Fock field. Our model incorporates Kerr-like non-linearity, parametric amplification, and intrinsic decoherence. By varying the photon-number cutoff, system dimensionality, and parametric amplification strength under different magnitudes of the Kerr effect, we analyze how these factors influence correlation dynamics and parameter estimation precision. We observe a threshold-like behavior in the photon number during the transition from a decoherence-dominated regime to a coherence-enhanced regime. These results show a balance between the amplification strength and Kerr effects, and reveal that GQD and QFI exhibit different levels of robustness. These findings provide valuable insights for optimizing non-linear atom-field configurations in quantum information and quantum metrology applications.