Optimal dense coding with mixed state entanglement
Tohya Hiroshima · Journal of Physics A Mathematical and General · 2001
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 χ* satisfies E R (ρ) ≤ χ* ≤ E R (ρ) + log 2 d , where E R (ρ) is the relative entropy of entanglement of the shared entangled state.