 Eve can then measure her photons in the correct basis and obtain information on the key without introducing detectable errors.Even with the possibility of a PNS attack a secure key can still be generated, as shown in the GLLP security proof; however, a much higher amount of privacy amplification is needed reducing the secure key rate significantly (with PNS the rate scales as formula_10 as compared to formula_11 for a single photon sources, where formula_11 is the transmittance of the quantum channel).There are several solutions to this problem.