How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.
We derive closed-form propagators for any
K-qubit subsystem of a closed
N-qubit network with a single conserved excitation. A single transition amplitude simultaneously controls excitation flow between subsystems, the positivity and complete positivity of every propagator, the entanglement entropy of every subsystem, and the quantum Fisher information for global parameters. Positivity and complete positivity coincide, determined solely by the direction of excitation flow, independently of subsystem size, coherence, or entanglement structure. A propagator is positive and completely positive if and only if it contracts the subsystem state toward its fixed point. The ensemble of propagators collectively constrains global properties inaccessible to any single subsystem. For single-qubit subsystems, we characterize the ensemble's fixed-point distribution and domain of positivity, finding a band of states that lies inside the positivity domain of every propagator yet is never visited by the physical dynamics. The quantum Fisher information decomposes into state and process contributions over any observation window
[t1,t2], with the state contribution bounded while the process contribution grows secularly. The total Fisher information is minimal when all future propagators are nonpositive and not completely positive, and near its maximum when they are positive and completely positive.