Optimal dimensionality for quantum cryptography

Two protocols are compared for sharing between Alice and Bob a cryptographic key composed from quarts. The first protocol uses a ququart (4-level system) prepared in one of 5 mutually biased bases. The second one uses two independent qubits, each being prepared in one of 3 mutually unbiased bases. Information gained by the eavesdropper Eve is calculated, suggesting that she uses an asymmetric cloner for cloning individual systems.