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The aim of this book is analysis of the polarization mode dispersion and the chromatic dispersion for the quantum cryptography on the phase coding method in a double Mach-Zehnder interferometry set-up, through some crucial examples of simulations. In this interferometric set-up system, communication is provided through fiber optics. Because of unavoidableness of dispersion appearances in fiber optics in real life, they should be handled with in optimum way. Examples show that how polarization mode dispersion and chromatic dispersion arise in optic systems, in which cases they should be most correlated.