Biphoton states in correlated turbulence

The effect of turbulence on a pair of photons propagating together through the same medium is analyzed. The behavior is compared to the case where these photons propagate separately through different turbulent media. The analysis is done with a multiple phase screen approach, by deriving and solving an infinitesimal propagation equation. We apply these results to the case where the initial photons are entangled in their spatial degrees of freedom with the aid of spontaneous parametric down-conversion. It is found that for this input state, the decay of entanglement in correlated media under the weak scintillation approximation is quicker than in uncorrelated media. Beyond the weak scintillation approximation, the entanglement in correlated media decays slower when it is close to zero --- approaching zero asymptotically as a function of scintillation strength. This is contrary to the case in uncorrelated media where entanglement becomes zero at a finite scintillation strength.