Quantum filtering equations for system driven by non-classical fields.

Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a system driven by non-classical states of light. We describe the stochastic evolution conditioned on the results of the quadrature measurement. The observed system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the non-classical states of the field: a combination of vacuum and single photon states and a mixture of two coherent states.