We derive a first-order differential equation for the decoherence of an orbital angular momentum entangled biphoton state propagating through a turbulent atmosphere. The derivation is based on the distortion that orbital angular momentum states experience due to propagation through a thin sheet of turbulent atmosphere. This distortion is treated as an infinitesimal transformation leading to a first-order differential equation, which we call an infinitesimal propagation equation. The equation is applied to a simple qubit case to show how the entanglement decays.
Reference:
Roux, FS. 2011. Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence. Physical Review A, Vol. 83(053822), pp. 11
Roux, F. (2011). Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence. http://hdl.handle.net/10204/5093
Roux, FS "Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence." (2011) http://hdl.handle.net/10204/5093
Roux F. Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence. 2011; http://hdl.handle.net/10204/5093.