(July 2001) | Nicolas J. Cerf,1,2 Mohamed Bourennane,3 Anders Karlsson,3 and Nicolas Gisin4
This paper explores the security of quantum key distribution (QKD) schemes using *qudits*, which are quantum states in a $d$-dimensional Hilbert space. Two protocols are considered: one using two mutually unbiased bases (an extension of the BB84 scheme) and another using all $d+1$ mutually unbiased bases (an extension of the six-state protocol for qubits). The authors derive the information gained by an eavesdropper applying a cloning-based individual attack and establish an upper bound on the error rate that ensures unconditional security against coherent attacks. They find that the 2-bases protocol is more secure due to its slightly higher acceptable error rate and larger secret key rate compared to the $(d+1)$-bases protocol. Additionally, they derive a simple security proof for QKD with qudits using an information inequality, which guarantees a non-zero secret key rate even under coherent attacks. The results suggest that higher-dimensional systems offer greater security advantages, but practical limitations such as detector efficiency and dark count rates may pose challenges in real-world applications.This paper explores the security of quantum key distribution (QKD) schemes using *qudits*, which are quantum states in a $d$-dimensional Hilbert space. Two protocols are considered: one using two mutually unbiased bases (an extension of the BB84 scheme) and another using all $d+1$ mutually unbiased bases (an extension of the six-state protocol for qubits). The authors derive the information gained by an eavesdropper applying a cloning-based individual attack and establish an upper bound on the error rate that ensures unconditional security against coherent attacks. They find that the 2-bases protocol is more secure due to its slightly higher acceptable error rate and larger secret key rate compared to the $(d+1)$-bases protocol. Additionally, they derive a simple security proof for QKD with qudits using an information inequality, which guarantees a non-zero secret key rate even under coherent attacks. The results suggest that higher-dimensional systems offer greater security advantages, but practical limitations such as detector efficiency and dark count rates may pose challenges in real-world applications.