We study the impact of errors from polarization rotation in optical fibers and detectors dark counts, in the calculation of the number of bits required for the estimation of the quantum-bit error rate (QBER), in a system of quantum communications. The encoding of bits is performed in photons polarization and the transmission channel is a standard single-mode fiber. The estimation of the QBER is defined considering a criterion of statistical level of confidence. A relation between the number of bits received and the number of bits that must be sent is also discussed. We conclude that: (i) the rotation of polarization presents the major contribution to errors and is as significative as bigger the fiber length and (ii) losses in fibers and optical devices together with a low quantum efficiency of single photon detectors contribute to large requirements of bits to be transmitted.