Orbital angular momentum (OAM) entangled bi-photons are a resource for the higher dimensional implementation
of quantum cryptography, which allows secure communication over various channels. In the case where
free-space is used as communication channel the initial OAM entangled bi-photon loses some or even all of its
entanglement because of the scintillation that it experiences while propagating through the turbulence in the
atmosphere. This decoherence of OAM entanglement has so far only been studied for the case of weak turbulence.
Unfortunately, it is the more challenging strong turbulence scenario that is relevant for the practical
implementation of free-space quantum communication through the atmosphere. Using an approach that differs
from previous approaches, we derive a master equation for the evolution of an OAM entangled bi-photon during
propagation through turbulence. However, in our approach the equation contains a derivative with respect to the
propagation distance instead of time. The principle is to consider the propagation over an infinitesimal distance
of OAM basis states through a random medium. This approach allows one to include, not only the effect of
turbulence of arbitrary strength, but also the effect of the inner and outer scale of the turbulence, as represented
by the Tartarskii and von Karman spectra. The resulting expression can predict the rates of decoherence for
arbitrary initial OAM entangled states and can be used to calculate the concurrence, which measures the amount
of entanglement, as a function of propagation distance for different initial entangled OAM states.