Identification of Unknown Parameters for a Class of Two-Level Quantum Systems

This technical note studies the identification of unknown decoherence rates for a class of two-level quantum systems undergoing spontaneous emission. Our previous work shows that estimates of the unknown decoherence rates can be obtained from the ensemble averages by imposing constant control and monitoring a sequence of identical systems continuously. Inspired by the work, this technical note further investigates the identification based on a single quantum system. It is shown that a mean-ergodic solution exists for a single system under constant control and convergence to an ergodic process can be guaranteed by introducing some noise into the control signals. The ensemble average can thus be replaced by the time average of a single system, and the parameter estimate can be obtained from a single implementation.