Quantum key distribution for d -level systems with generalized Bell states

Using the generalized Bell states and controlled-NOT gates, we introduce an entanglement-based quantum key distribution (QKD) of d-level states (qudits). In case of eavesdropping, Eve's information gain is zero and a quantum error rate of $(d\ensuremath{-}1)/d$ is introduced in Bob's received qudits, so that for large d, comparison of only a tiny fraction of received qudits with the sent ones can detect the presence of Eve.