Comparative characteristics of quantum key distribution protocols with alphabets corresponding to the regular polyhedrons on the Bloch sphere

摘要

Possibilities of improving characteristics of quantum key distribution (QKD) protocols via variation of character set in quantum alphabets are investigated. QKD protocols with discrete alphabets, letters of which form regular polyhedrons on the Bloch sphere (tetrahedron, octahedron, cube, icosahedron, and dodecahedron, which have 4, 6, 8, 12, and 20 vertexes), and QKD protocol with continuous alphabet, which corresponds to the limiting case of a polyhedron with infinitive number of vertexes, are considered. Stability of such QKD protocols to the intercept-resend and optimal eavesdropping strategies at the individual attacks, is studied in detail. It is shown that in case of optimal eavesdropping strategy, after safety bases reconciliation, critical error rate of the QKD protocol with continuous alphabet surpasses all other protocols. Without basis reconciliation the highest critical error rate have the protocol with tetrahedron-type alphabet.