Phase damping destroys quantum Fisher information of W states

• Quantum Fisher information of W states under decoherence channels studied.
• Found zero Fisher information of W states in z direction.
• Found sudden drop as W states go under amplitude damping.
• Found zero Fisher information of W states under phase damping.

We study the quantum Fisher information (QFI) of W states in the basic decoherence channels. We show that, as decoherence starts and increases, under i) depolarizing, QFI smoothly decays; ii) amplitude damping, QFI first exhibits a sudden drop to the shot noise level, then decreases to zero and finally increases back to the shot noise level; iii) phase damping, QFI is zero for all non-zero decoherence. We also find that on the contrary to GHZ states, QFI of W states in x and y directions are equal to each other and zero in z direction.