A comparative study of the P and Q representations of a feedback controlled two-qubit system

In this Letter the Master equation of a two qubit system is transformed into Fokker-Planck equations in order to find the Glauber-Sudarshan P function representation. For the two qubit system examined in this Letter, the P representation is ill defined, which indicates the system is non-classical. A qualitative measure of the non-classical nature of the system is found by taking the semi-classical limit of the Fokker-Planck equation and obtaining a simplified Glauber-Sudarshan P representation. The agreement between the simplified P representation and the Q representation as well as the system stability are discussed when feedback is present and absent.