Optimal dense coding with mixed state entanglement (Q2766206)

The author investigates dense coding with a general mixed state on the Hilbert space \(C^d\otimes C^d\) 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 \(\chi^*\) satisfies \(E_R(\rho)\leq \chi^*\leq E_R(\rho)+\log_2d\), where \(E_R(\rho)\) is the relative entropy of entanglement of the shared entangled state.