  In this paper, we have investigated the preservation of quantum Fisher
information of a single-qubit system coupled to a common zero temperature
reservoir through the addition of noninteracting qubits. The results show that,
the QFI is completely protected in both Markovian and non-Markovian regimes by
increasing the number of additional qubits. Besides, the phenomena of QFI
display monotonic decay or non-monotonic with revival oscillations depending on
the number of additional qubits in a common dissipative reservoir. Moreover, we
extend this model to investigate the effect of additional qubits N-1 and the
initial conditions of the system on the geometric phase. It is found that, the
robustness of GP against the dissipative reservoir has been demonstrated by
increasing gradually the number of additional qubits. Besides, the GP is
sensitive to the initial parameter theta, and possesses symmetric in a range
regime 0,2 pi.
