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