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In this paper we consider the Liouville equation that describes the quantum nonunitary dynamics of quantum states in optical fiber. We consider a particular case of thermalization aiming to applications related to various quantum information protocols; however, the model can be generalized in various ways taking into account more features (external pump, nonlinear interactions, continuous spectra, free space propagation, etc.). In order to obtain the appropriate evolution models for states in the channel we use the su (1, 1) algebra formalism in the Liouville representation. The developed model is applied in cases of two different initial states as an example. The first is single-and multifrequency-mode (eg, wavelength-division-multiplexed) weak coherent states in quantum notation as a rather simple but useful example. This particular example is of interest since weak coherent states are a commonly used tool in …