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Estimating dynamic parameters quantumly

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I will give an overview of two ways to estimate parameters with a quantum system when the dynamics is nontrivial. In the first case, the parameter is changing in an irregular way, and we use consider the use of continuous measurement to track it in time. Tracking speed is of the essence for feedback purposes, and I will present our new and improved way to speed up the estimation algorithm. In the second case, I will consider the use of Hamiltonian control to estimate a fixed parameter, but of a time-dependent Hamiltonian. In this case established scaling bounds on the quantum Fisher information can be broken, and the quantum control is needed to do it. A simple spin example will be given to illustrate the general results.