Fe b 20 03 Security of Quantum Key Distribution with entangled qu N its

In this paper we consider a generalisation of Ekert’s entanglement-based quantum cryptographic protocol where qubits are replaced by quN its (i.e., N -dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. For doing so, we generalize Cerf’s formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We show that when Alice and Bob compare the signal obtained in 100 % correlated bases and the remaining signal, they are able to thwart attacks based on state-dependent or nonuniversal cloning machines. This result sheds a new light on previously obtained upper bounds on the error rate that guarantees the confidentiality of qubits and qutrits Ekert’s protocols.