The scientists theoretically study quantum parameter estimation in quantum chaotic systems. The analysis is based on an effective description of quantum ergodic systems in terms of a random matrix Hamiltonian. Based on this approach, researchers derive an analytical expression for the time evolution of the quantum Fisher information (QFI), which is found to have three distinct timescales. Initially, the QFI increase is quadratic in time, characterising the timescale over which initial information is extractable from local measurements only. This quickly passes into linear increase with slope determined by the decay rate of the measured spin observable. When the information is fully spread among all degrees of freedom, a second quadratic timescale determines the long-time behaviour of the QFI. Scientists test random matrix theory prediction with the exact diagonalisation of a nonintegrable spin system, focusing on the estimation of a local magnetic field by measurements of the many-body state. The numerical calculations agree with the effective random matrix theory approach and show that the information on the local Hamiltonian parameter is distributed throughout the quantum system during the quantum thermalisation process.