Lindblad equation for the decay of entanglement due to atmospheric scintillation

Abstract

The quantum state for the spatial degrees of freedom of photons propagating through turbulence is analyzed. The turbulent medium is modeled by a single phase screen for weak scintillation conditions and by multiple phase screens for general scintillation conditions. In the former case the process is represented by an operator product expansion, leading to an integral expression that is consistent with current models. In the latter case the evolution of the density operator is described by a first order differential equation with respect to the propagation distance. It is shown that this differential equation is expressed in the Lindblad form, prior to the evaluation of the ensemble averages. After the evaluation of the ensemble averages the equation takes on the form of the infinitesimal propagation equation.