Dynamics of the uncertainty value of quadratures for bosonic quantum states

In this work we consider the time evolution of the mean values of the first and second moments of the quadrature operators for an arbitrary bosonic quantum state in a single mode transmitted through an optical fiber channel. We utilize the density matrix formalism and the open quantum systems theory and investigate Lindblad master equation in order to derive expressions for the dynamics of mentioned field observables. Obtained expressions contain terms characterized by high frequency oscillations. For the purpose of elimination of these terms we find the envelope functions for the values of the first and second moments of the quadrature operators.