  We study the stability under quantum noise effects of the quantum privacy
amplification protocol for the purification of entanglement in quantum
cryptography. We assume that the E91 protocol is used by two communicating
parties (Alice and Bob) and that the eavesdropper Eve uses the isotropic
Bu\v{z}ek-Hillery quantum copying machine to extract information. Entanglement
purification is then operated by Alice and Bob by means of the quantum privacy
amplification protocol and we present a systematic numerical study of the
impact of all possible single-qubit noise channels on this protocol. We find
that both the qualitative behavior of the fidelity of the purified state as a
function of the number of purification steps and the maximum level of noise
that can be tolerated by the protocol strongly depend on the specific noise
channel. These results provide valuable information for experimental
implementations of the quantum privacy amplification protocol.
