The relative entropy as a tool to analyze the intrusion based on Bužek-Hillery machine

The intrusion based on Bužek-Hillery universal quantum copying machine (UQCM) is investigated. A major problem to the eavesdropper Eve is how to choose the intrusion parameters required by the copying machine in order to take out the maximum of information on the transmitted qubits. In the present paper, only the isotropic cloning is considered. The degree of intrusion is evaluated by means of the ratios of the receiver (Bob) coordinates and the eavesdropper (Eve) coordinates to the sender (Alice) coordinates in the Bloch sphere as well as by means of relative entropy of Bob with respect to Eve. For isotropic cloning, the relative entropy of Bob with respect to Eve is independent of the state sent by Alice. The relative entropy of Bob with respect to Eve proves to be minimal at the maximal degree of intrusion. This study shows that the relative entropy may be a valuable tool to measure the intrusion.