Quantum Fisher information,derived from the classical Fisher information, is closely related to the quantum entanglement in quantum information. The entanglement and the quantum information which are both associated with the classical phase space are investigated in a two-component Bose-Einstein condensate impacted by the impulses. The results reveal that the states regardless of disorder of the phase space after the first impulse are entangled. However, the quantum information is very sensitive to the state centred in the classical phase space, concretely, the value of the quantum information centred in the chaotic region is greater than in the regular region. By employing the good quantum-classical correspondence, we conclude that the quantum information can serve as a signature of the quantum chaos.