Admissible Optimal Control for Parameter Estimation in Quantum Systems

This letter investigates parameter estimation in quantum systems that undergo dynamical evolution. Optimal control problems are formulated to maximize the information, about an unknown parameter, extracted by a given quantum measurement apparatus. This letter introduces the concept of “admissible controls”—control laws that do not depend on the unknown parameter they elicit. For scalar parameter estimation in unital quantum systems interrogated by binary measurements, this letter derives a necessary and sufficient condition on quantum measurement operators so that an information maximizing control law is admissible. When the admissibility condition is satisfied, it is shown that the resulting optimal control problem may be solved using well-established techniques.