Quantum Cryptography with Entangled QuNits

We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N-dimensional Hilbert space. In our protocol, we adopt asymmetric measurement scheme resulting in an efficiency higher than previous protocols and a generalized Bell inequality [Phys. Rev. Lett.92(2004)130404] is employed to detect the presence of an eavesdropper Eve. We also derive the information gained by a potential eavesdropper Eve applying a cloning-based attack and the maximal error rate which measures the robustness of the protocol. The result shows that the security of our scheme increases with the dimension N.