Optimal Eavesdropping in Quantum Cryptography with Six States

A generalization of the quantum cryptographic protocol by Bennett and Brassard is discussed, using three conjugate bases, i.e., six states. By calculating the optimal mutual information between sender and eavesdropper it is shown that this scheme is safer against eavesdropping on single qubits than the one based on two conjugate bases. We also address the question for a connection between the maximal classical correlation in a generalized Bell inequality and the intersection of mutual informations between sender/receiver and sender/eavesdropper.