Optimal dense coding with mixed state entanglement

I investigate dense coding with a general mixed state on the Hilbert space C^d\ C^d shared between a sender and receiver. The following result is proved. When the sender prepares the signal states by mutually orthogonal unitary transformations with equal \ a priori probabilities, the capacity of dense coding is maximized. It is also proved that the optimal capacity of dense coding \ ^* satisfies Eₑ (\) \ \ ^*\ Eₑ (\) +\₂d, where Eₑ (\) is the relative entropy of entanglement of the shared entangled state.