Security proof for qudit-system-based quantum cryptography against entanglement-measurement attack

Entanglement-measurement attack is a well-known attack in quantum cryptography. In quantum cryptography protocols, eavesdropping checking can resist this attack. There are two known eavesdropping checking methods. One is to use decoy photon technology for eavesdropping checking. The other is to use the entanglement correlation of two groups of non-orthogonal entangled states for eavesdropping checking. In this paper, we prove the security against entanglement-measurement attack for the qudit-system-based quantum cryptography protocols which use the two methods for eavesdropping checking. Our security proof is useful to improve the eavesdropping checking method used in quantum cryptography protocols.