Quantum key distribution with no shared reference frame

Any quantum communication task requires a common reference frame (i.e., phase, coordinate system). In particular, quantum key distribution requires different bases for preparation and measurements of states which are obviously based on the existence of a common frame of reference. Here, we showhowQKDcan be achieved in the absence of any common frame of reference. We study the coordinate reference frame, where the two parties do not even share a single direction, but the method can be generalized to other general frames of reference, pertaining to other groups of transformations.