Entanglement-assisted alignment of reference frames using a dense covariant coding

A dense covariant coding was used for the entanglement-assisted alignment of a reference frames. A procedure inspired by dense coding was presented which enables a highly efficient transmission of information of a continuous nature. The optimal covariant measurement was found and the corresponding average error was computed, which have a simple close form. A covariant scheme for transmitting continuous information efficiently through a quantum channel was also presented.