Quantum model of decoherence in the polarization domain for the fiber channel

Abstract

In this work we consider the Liouville equation; it describes the dynamics of the photon density matrix in the Schr\odinger representation based on the Markov approximation in the channel without dispersion. The equation contains a relaxation superoperator dependent on the phenomenological parameters of the optical fiber. These parameters allow one to take into account the phenomena of birefringence and optical activity, isotropic absorption, and dichroism. We also present in our work that these parameters affect not only the polarization of the states but the length of the Stokes vector. Hence the developed technique describes the decoherence process in the polarization domain in the quantum case and allows one to analyze the dynamics of single-photon states in the quantum (depolarizing) channel more properly. We also present a visual illustration of polarization states' evolution in the polarization-coded quantum key distribution BB84 protocol as an example. We estimate quantum bit error rates' dependence on channel length. Also we examine maximal allowed channel length, dependent on various configurations of channel parameters.