MISCELLANEOUS

The efficiency of repeaters based on the Einstein-Podolsky-Rosen effect for quantum cryptography in a damping channel

S. N. Molotkov

Institute of Solid State Physics, Russian Academy of Sciences

Abstract: Based on the fundamental Holevo inequality and on the direct calculations, it is argued that the number of commitments required per one bit in a key in a damping channel increases exponentially with channel length. It is shown that the conclusion drawn recently by Duan $et~al.$ [4] that the exponential increase in resources for quantum cryptography in a damping channel can be reduced to the polynomial law by generating a through Einstein-Podolsky-Rosen pair is erroneous. Therefore, the results of [4] do not solve the fundamental problem restricting practical application of quantum cryptography at distances larger than the damping length.

PACS: 03.65.Bz, 42.50.Dv, 89.70.+c

Received: 30.10.2001

 English version: Journal of Experimental and Theoretical Physics Letters, 2001, 74:10, 517–521

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