Quantum Fisher Information of Superpositions with 3-Qubit Ghz-Class State and W State

We investigate the quantum Fisher information in a general superposition of a GHZ-class state and a W state. It is shown that the mean spin direction is determined by the four coefficients of superposition and the relative phase between the GHZ-class state and the W state and it is independent of the relative phase between the GHZ-class state; while the length of mean spin is only determined by the four superposition coefficients. It is also shown that the quantum Fisher information of the superposition state is determined by the four superposition coefficients and the two relative phases.