Relativistic corrections to photonic entangled states for the space-based quantum network

In recent years there has been a great deal of focus on a globe-spanning quantum network, including linked satellites for applications ranging from quantum key distribution to distributed sensors and clocks. In many of these schemes, relativistic transformations may have deleterious effects on the purity of the distributed entangled pairs. In this paper, we make a comparison of several entanglement distribution schemes in the context of special relativity. We consider three types of entangled photon states: polarization, single photon, and Laguerre-Gauss mode entangled states. All three types of entangled states suffer relativistic corrections, albeit in different ways. These relativistic effects become important in the context of applications such as quantum clock synchronization, where high fidelity entanglement distribution is required.