In this paper, the quantum theory of the measurement of the intensity difference between two light beams is analysed. The quantum noise can be reduced by increasing the photon correlation between two beams. For anti-Cauchy-Schwarz light, another type of nonclassical radiation fields, this quantum noise can be reduced to a level below the classical limit. The sub-shot noise may occur in DFWM between the conjugate wave and the transmit wave.