Fiber-optic parametric amplifiers and optical wavelength convertors based on four-wave mixing (FWM) process in optical fibers are important issues in modern optical communication systems for signal processing applications. In this paper we study theoretically and experimentally the FWM process in optical fibers in a low power regime. We explore the dependence of the FWM efficiency on the relative state of polarization of all optical signals involved in this nonlinear process, to experimentally obtain the transition region between an almost co-polarized situation and a decorrelated state of polarization. Results show the need of considering the polarization dependent effects in the scalar FWM theory in order to obtain an accurate description of this nonlinear process. The 8/9 coefficient for the nonlinear parameter is observed by direct measurement of the optical power of the idler wave, which indicates that the polarization of the optical fields are mostly decorrelated. Results also show that the randomly state of polarization variation in the fiber leads to a loss of efficiency in the FWM process. That loss can be seen as a reduction of the value of the fiber nonlinear parameter.