Quantum filtering for multiple measurements driven by two single-photon states

In this paper, the problem of quantum filtering with two homodyne detection measurements for a two-level system has been considered. The quantum system is driven by two input light field channels, each of which contains a single photon. A quantum filter based on multiple measurements is designed; both the master equations and stochastic master equations are derived. In addition, numerical simulations for master equations with various pulse shape parameters are also compared.