In this thesis we explain the approach of teleporting the polarisation states of photons emitted by two remote quantum dots. The reader is guided through the theory of teleportation, including the concepts of entanglement and the Bell state measurement of two photons. In this context we explain the way of statistically proving successful quantum teleportation. We include numerical simulations, which allows us to gather a better insight to the numerous challenges arising. Subsequently we investigate the GaAs quantum dots as deterministic sources of entangled single photons and why they are suitable for our purpose. We address their fabrication and energetic structure, as well as their excitation, the emission properties and imperfections, affecting the quality of teleportation. We describe the fabrication of a device capable of exerting elastic stress to the host matrix of the quantum dots. This allows us to precisely match the emission energies of two remote quantum dots. Further, we point out the measures taken to prepare the experimental optical setup, enabling the first experiments of teleportation done so far in our institute. We conclude the thesis by showing preliminary results, evaluated by a self written software.