A unified framework for fault tolerant quantum filtering and fault detection

A quantum-classical probability space model is developed for a class of open quantum systems where the system dynamics involve both classical and quantum random variables. This model provides a unified framework for analyzing open quantum systems subject to stochastic faults. A fault tolerant quantum filter and a fault detection equation are simultaneously derived for this class of open quantum systems using a reference probability approach. A two-level open quantum system subject to Poisson-type faults is presented to illustrate the proposed method. These results have the potential for the systematic development of new fault tolerant control theory for quantum systems.