  Quantum-cryptography key distribution (QCKD) experiments have been recently
reported using polarization-entangled photons. However, in any practical
realization, quantum systems suffer from either unwanted or induced
interactions with the environment and the quantum measurement system, showing
up as quantum and, ultimately, statistical noise. In this paper, we investigate
how ideal polarization entanglement in spontaneous parametric downconversion
(SPDC) suffers quantum noise in its practical implementation as a secure
quantum system, yielding errors in the transmitted bit sequence. Because all
SPDC-based QCKD schemes rely on the measurement of coincidence to assert the
bit transmission between the two parties, we bundle up the overall quantum and
statistical noise in an exhaustive model to calculate the accidental
coincidences. This model predicts the quantum-bit error rate and the sifted key
and allows comparisons between different security criteria of the hitherto
proposed QCKD protocols, resulting in an objective assessment of performances
and advantages of different systems.
