QUANTUM INFORMATION SCIENCE

On the maximum admissible error and key compression degree in quantum cryptography on two nonorthogonal states

S. N. Molotkov<sup>ab

a</sup> Institute of Solid State Physics, Russian Academy of Sciences
^b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The extreme admissible error probability at the receiving end to which the secure key distribution is possible has been found. This result takes into account all possible attacks on the distributed key, including those that involve large quantum memory and the capability of an eavesdropper to perform collective measurements simultaneously over the entire transmitted sequence of quantum states. The critical error is independent of the parameters of a particular attack and is determined only in terms of the overlapping degree $\varepsilon=|\langle u_1|u_0\rangle|$ of information states and the fundamental functions of classical and quantum information theories. The latter functions are the capacity ($H(Q)$~-- of a classical binary communication channel and classical capacity ~-- $\overline{C}(\varepsilon)$ ) of a binary quantum communication channel. The key compression degree after error correction is also expressed in terms of only the classical capacity $\overline{C}(\varepsilon)$ of the quantum communication channel.

PACS: 03.67.Dt, 42.50.-p, 89.70.+c

Received: 11.04.2005
Revised: 11.05.2005

 English version: Journal of Experimental and Theoretical Physics Letters, 2005, 81:11, 599–604

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