Optimal dense coding with mixed state entanglement

I investigate dense coding with a general mixed state on the Hilbert space C(d)xC(d) shared between a sender and receiver. The following result is pro ved. When the sender prepares the signal states by mutually orthogonal unit ary transformations with equal a priori probabilities, the capacity of dens e coding is maximized. It is also proved that the optimal capacity of dense coding chi* satisfies E-R (rho) less than or equal to chi* less than or eq ual to E-R (rho) + log(2) d, where E-R (rho) is the relative entropy of ent anglement of the shared entangled state.