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Quantum Fisher information and its super additivity in an anisotropic quantum Rabi model

In this paper, we study the additivity of quantum Fisher information (QFI) in a coupled system composed by a two-level system and a bosonic mode, which is described by an anisotropic Rabi model. Utilizing a unitary transformation approach, we obtain the approximate ground state for the global state and the reduced density matrix for each subsystem. We find the additivity of QFI, that is, the summation of QFI for two subsystems is always larger than that of the global system. We hope our work will stimulate the studies of quantum metrology in hybrid system.