Fidelity analysis of quantum cloning based attacks in quantum cryptography

In quantum cryptography the encoded pure quantum states are sent through a quantum communication channel. An eavesdropper can not measure the sent qubit, since the result of the measurement is one of the single quantum system's eigenstates. The best eavesdropping attacks for quantum cryptography use the cloning machines. In this paper, we show an effective method to compute the fidelity of quantum cloning based attacks in quantum cryptography, using Delaunay tessellation. We extend our method to study the fidelity of optimal cloning of mixed states in quantum cryptography.