Fault tolerant design of quantum filter for a class of open quantum systems with photon counting measurement

In [Q. Gao, D. Dong, and I. R. Petersen, "Fault tolerant quantum filtering and fault detection for quantum systems," arXiv:1504.06780 [math-ph], 2015], a quantum-classical probability space model has been proposed to solve the problem of fault tolerant quantum filtering and fault detection for a class of laser-atom open quantum systems subject to stochastic faults and under homodyne detection. This paper further investigates the case when performing photo counting measurements on the laser field.