  The evolution of high dimensional entanglement in atmospheric turbulence is
investigated. We study the effects of turbulence on photonic states generated
by spontaneous parametric down-conversion, both theoretically and
experimentally. One of the photons propagates through turbulence, while the
other is left undisturbed. The atmospheric turbulence is simulated by a single
phase screen based on the Kolmogorov theory of turbulence. The output after
turbulence is projected into a three-dimensional (qutrit) basis composed of
specific Laguerre-Gaussian modes. A full state tomography is performed to
determine the density matrix for each output quantum state. These density
matrices are used to determine the amount of entanglement, quantified in terms
of the negativity, as a function of the scintillation strength. Theoretically,
the entanglement is calculated using a single phase screen approximation. We
obtain good agreement between theory and experiment.
