Quantum state transfer through time reversal of an optical channel

Rare-earth ions have exceptionally long coherence times, making them an excellent candidate for quantum information processing. A key part of this processing is quantum state transfer. We show that perfect state transfer can be achieved by time reversing the intermediate quantum channel, and suggest using a gradient echo memory (GEM) to perform this time reversal. We propose an experiment with rare-earth ions to verify these predictions, where an emitter and receiver crystal are connected with an optical channel passed through a GEM. We investigate the effect experimental imperfections and collective dynamics have on the state transfer process. We demonstrate that super-radiant effects can enhance coupling into the optical channel and improve the transfer fidelity. We lastly discuss how our results apply to state transfer of entangled states.