Security of quantum key distribution using d-level systems

Phys Rev Lett. 2002 Mar 25;88(12):127902. doi: 10.1103/PhysRevLett.88.127902. Epub 2002 Mar 8.


We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e., quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all d+1 available such bases (extending the six-state protocol for qubits). We derive the information gained by a potential eavesdropper applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.