For fiber-based polarization entangled photon pairs generated by four-wave mixing nonlinear effect, a common method to process coincidence counts and reconstruct density matrix of original quantum states is maximum likelihood estimation. Pump power is an essential parameter to investigate throughout the process of entanglement generation, correlation detection and quantum state tomography. Defined as the optical power of input laser pulses that enter dispersion-shifted fiber and generate entangled pairs, pump power directly affects single counts rates for both signal and idler. As noise rate changes accordingly, coincidence to accidental counts ratio does not necessarily increase with more detected counts. We derive relation between pump power and entangled correlation. Because different power is associated with different order of susceptibility, we also study its effect on entangled photon generation rate. Transmission rate through fibers, filters, polarizing beam splitters and other optical components as well as the detection efficiency at each avalanche photodiode are taken into consideration because they contribute to the reliability of photon counting statistics. System error such as measuring basis error is studied whether it is amplified, suppressed or remain invariant with pump power modification. Many parameters’ relations with pump power cannot be simply described as a one-line equation. Therefore, we explain those relations in detail and propose a method of finding a suitable pump power within given circumstances that would serve reconstructing the most accurate quantum state.