Risk-sensitive performance criteria and robustness of quantum systems with a relative entropy description of state uncertainty

TL;DR

This paper explores the relationship between risk-sensitive performance criteria and robustness in quantum control systems, using quantum relative entropy to quantify state uncertainty and guide robust control design.

Contribution

It establishes a connection between quantum risk-sensitive criteria and robustness to state uncertainty, extending classical minimax control concepts to quantum systems.

Findings

Link between risk-sensitive and robust quantum control established

Quantum relative entropy used to quantify state uncertainty

Guidelines for choosing risk-sensitivity parameters in quantum control

Abstract

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.