LZ12888 - How do motion and gravity affect quantum information tasks? In 2012 a teleportation protocol was successfully performed across 143km between two Canary Islands by A. Zeilinger’s group. In this experiment, time and positions were determined accurately employing the Global Positioning System (GPS), which is a system of satellites used for time dissemination and navigation. It is well known that GPS takes into account Einstein's theory of relativity to achieve the required precision. However, relativistic effects over the basic resource of the experiment -quantum entanglement- were not considered. Motivated by the success of this kind of tests, space agencies are investing resources for the implementation of space-based quantum communications. At these regimes, relativistic effects can no longer be ignored. In our Letter, we show that relativistic motion and gravity have observable effects in the quantum teleportation protocol. Indeed they can decrease its efficiency; however, we explain how the errors can be corrected. We propose a physical implementation of our relativistic teleportation protocol, which is well within reach of cutting-edge technology using superconducting circuits. The realization of this low-cost tabletop experiment, demonstrating for the first time the effects of relativity on quantum information tasks, will inform expensive space-based programs.
