Dense coding for continuous variables

A scheme to achieve dense quantum coding for the quadrature amplitudes of the electromagnetic field is presented. The protocol utilizes shared entanglement provided by nondegenerate parametric down-conversion in the limit of large gain to attain high efficiency. For a constraint in the mean number of photons \(\bar n\) associated with modulation in the signal channel, the channel capacity for dense coding is found to be \(1 + \bar n + {\bar n^2}\), which always beats coherent-state communication and surpasses squeezed-state communication for \(\bar n > 1\). For \(\bar n > > 1\), the dense coding capacity approaches twice that of either scheme.