Quantum Fisher Information of Several Qubitsin the Superposition of A GHZ and two W Stateswith Arbitrary Relative Phase

We study the quantum Fisher information (QFI) of a system of several particles which is in a superposition of a GHZ and two W states with arbitrary relative phase. We show that as the number of particles increases from 3 to 4, the behavior of QFI drastically changes. We also show how the dependence of QFI on the relative phase weakens as the number of particles increases. We also analyze the QFI for the state for several instances of N due to the change of the relative phases