Security of Quantum Key Distribution Using [Formula presented]-Level Systems

We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e., quantum states in a [Formula presented]-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all [Formula presented] 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.