Risk-sensitive performance criteria and robustness of quantum systems with a relative entropy description of state uncertainty
For researchers in quantum control, this work offers a theoretical framework connecting risk-sensitive control and robustness, but it is largely theoretical and incremental.
The paper establishes links between risk-sensitive performance criteria and robustness in quantum control systems, using quantum relative entropy to model state uncertainty, analogous to classical minimax LQG control. It provides a rational basis for choosing the risk-sensitivity parameter in robust quantum control.
This paper considers links between the original risk-sensitive performance criterion for quantum control systems and its recent quadratic-exponential counterpart. We discuss a connection between the minimization of these cost functionals and robustness with respect to uncertainty in system-environment quantum states whose deviation from a nominal state is described in terms of the quantum relative entropy. These relations are similar to those in minimax LQG control for classical systems. The results of the paper can be of use in providing a rational choice of the risk-sensitivity parameter in the context of robust quantum control with entropy theoretic quantification of statistical uncertainty in the system-field state.