Secure and robust transmission and verification of unknown quantum states in Minkowski space

An important class of cryptographic applications of relativistic quantum information work as follows. B generates a random qudit and supplies it to A at point P. A is supposed to transmit it at near light speed c to to one of a number of possible pairwise spacelike separated points Q1, …, Qn. A's transmission is supposed to be secure, in the sense that B cannot tell in advance which Qj will be chosen. This poses significant practical challenges, since secure reliable long-range transmission of quantum data at speeds near to c is presently not easy. Here we propose different techniques to overcome these diffculties. We introduce protocols that allow secure long-range implementations even when both parties control only widely separated laboratories of small size. In particular we introduce a protocol in which A needs send the qudit only over a short distance, and securely transmits classical information (for instance using a one time pad) over the remaining distance. We further show that by using parallel implementations of the protocols security can be maintained in the presence of moderate amounts of losses and errors.