Wigner Function in Phase Coding QKD

Phase coding systems in quantum cryptography use two largely separated fiber glass Mach-Zehnder (MZ) interferometers which belong to Alice and Bob, respectively. If both partners adjust their phase shifters accordingly, the time pulses behind the second MZ interferometer exhibit interference effects which can be applied to the encoding-decoding procedure in quantum key distribution. Using Gaussian wave packets, the energy and time spectra of those interference effects are analyzed by means of the Wigner function taking into account the wave length distribution, chromatic dispersion, absorption and the dimensions of the interferometric set-up.