Optimal dense coding with mixed state entanglement

Abstract

I investigate 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 {\it a priori} probabilities, the capacity of dense coding is maximized. It is also proved that the optimal capacity of dense coding ${\chi }^{\ast }$ satisfies $E_R(\rho )\le {\chi }^{\ast }\le E_R(\rho )+{\log }_{2}d$, where $E_R(\rho )$ is the relative entropy of entanglement of the shared entangled state.

Revised. To appear in J. Phys. A: Math. Gen. (Special Issue: Quantum Information and Computation). LaTeX2e (iopart.cls), 8 pages, no figures

References in corpus (2)

• Dense Coding for Continuous Variables
• Operator monotones, the reduction criterion and the relative entropy

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