Quantum Fisher information of a parameter characterizes the sensitivity of the state with respect to changes of the parameter. In this article, we study the quantum Fisher information of a state with respect to $\mathrm{SU}\left(2\right)$ rotations under three decoherence channels: the amplitude-damping, phase-damping, and depolarizing channels. The initial state is chosen to be a Greenberger-Horne-Zeilinger state of which the phase sensitivity can achieve the Heisenberg limit. By using the Kraus operator representation, the quantum Fisher information is obtained analytically. We observe the decay and sudden change of the quantum Fisher information in all three channels.

• Received 29 March 2011
• Corrected 28 September 2011

DOI:https://doi.org/10.1103/PhysRevA.84.022302