Geometrical analysis of physically allowed quantum cloning transformations for quantum cryptography

The security of quantum key distribution (QKD) relies on the no-cloning theorem, which allows no to copy perfectly a quantum system. An eavesdropping activity on the quantum channel perturbs the state of the quantum states, which results in noise at the receiver. The physical layer detection of the eavesdropping activity of the quantum channel requires tomography, which is intractable in experiment. An adequate and equivalent answer for the problem can be proposed through the logical layer. We propose an efficient algorithmical tool to study the eavesdropping activity on the quantum channel and characterize the properties of a quantum cloning-based attack for DV and CVQKD protocols. The physically allowed quantum cloning transformations on a quantum system can be described in terms of information geometry. We propose a computational geometrical method to analyze the cloning activity on the quantum channel and to characterize the noise properties. The security analysis studies the DV (discrete variable) and CV (continuous variable) QKD schemes through the four-state (BB84) and six-state DVQKD protocols and the two-way CVQKD protocol. The proposed geometrical method provides a useful tool to analyze the most powerful attacks against quantum cryptography and the effects of the physically allowed quantum cloning transformations.