Efficient Computational Information Geometric Analysis of Physically Allowed Quantum Cloning Attacks for Quantum Key Distribution Protocols

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Executive Summary

In secret quantum communications the best eavesdropping attacks on quantum cryptography are based on imperfect cloning machines. The incoherent attack, based on quantum cloning, is the most common eavesdropping strategy. Using a probe, the eavesdropper imperfectly clones the sender's quantum state which keeps one copy and sends the other. The physically allowed transformations of Eve's quantum cloner on Bob's qubit can be described in terms of Completely Positive (CP), trace preserving maps. The map of the quantum cloner compresses the Bloch-ball, as an affine map. This affine map has to be a complete positive, trace preserving map, which shrinks the Bloch ball. The effects of a quantum cloner can be given in tetrahedron representation.

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