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 $\mathrm{n̄}$ associated with modulation in the signal channel, the channel capacity for dense coding is found to be $\ln (1+\mathrm{n̄}+n^2),$ which always beats coherent-state communication and surpasses squeezed-state communication for $\mathrm{n̄}>1.\mathrm{}$ For $\mathrm{n̄}\gg 1,$ the dense coding capacity approaches twice that of either scheme.