Unconditionally Secure Key Distribution In Higher Dimensions By   Depolarization
  This paper presents a prepare-and-measure scheme using $N$-dimensional quantum particles as information carriers where $N$ is a prime power. One of the key ingredients used to resist eavesdropping in this scheme is to depolarize all Pauli errors introduced to the quantum information carriers. Using the Shor-Preskill-type argument, we prove that this scheme is unconditionally secure against all attacks allowed by the laws of quantum physics. For $N = 2^n > 2$, each information carrier can be replaced by $n$ entangled qubits. In this case, there is a family of eavesdropping attacks on which no unentangled-qubit-based prepare-and-measure quantum key distribution scheme known to date can generate a provably secure key. In contrast, under the same family of attacks, our entangled-qubit-based scheme remains secure whenever $2^n \geq 4$. This demonstrates the advantage of using entangled particles as information carriers and of using depolarization of Pauli errors to combat eavesdropping attacks more drastic than those that can be handled by unentangled-qubit-based prepare-and-measure schemes. 
H. F. Chau