Optimal controls in many-body quantum metrology

Quantum metrology is the subject of improving the precision of parameter estimation using quantum effects. Quantum controls come into play in quantum metrology in that they can engineer the dynamics and therefore alter the generator for parameter estimation. Assuming controls Hamiltonians are freely available, there has been a mature theory developed for applying quantum control in quantum metrology. However, how to apply optimal quantum controls in quantum metrology when certain control Hamiltonians are not available? In this talk, we answer this question by deriving optimal control equations using the variational approach. When the estimation Hamiltonian is time-independent, we show that one can apply the high-frequency expansion to recover the Heisenberg scaling for time-independent Hamiltonians. For example, for a spin chain with interactions up to local three-body interactions, assuming one-body and two-body controls are at hand, one can cancel the effect of local three-body interactions with high-frequency drives consisting of local two-body interactions. Our results open the door to investigate quantum metrology with a constrained set of available controls, which can be very practical for many-body quantum metrology.