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arXiv:quant-ph/0101105

Quantum Bit Commitment in a Noisy Channel

S. N. Molotkov, S. S. Nazin

Published Jan 22, 2001• 0 citations
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Abstract

Under rather general assumptions about the properties of a noisy quantum channel, a first quantum protocol is proposed which allows to implement the secret bit commitment with the probability arbitrarily close to unity.
DOI
10.48550/arxiv.quant-ph/0101105

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The bit commitment can be realized by using a noisy channel. Winter-Nascimento-Imai showed that the bit commitment capacity of a noisy channel is given by Cb= maxpNH(X\Y) where X and Y are the input and output of the channel. In this paper, the idea of a multiplex coding, which was first introduced into the coding problem of a wiretap channel by Kobayashi-Yamamoto-Ogawa, is applied to the bit commitment coding. The coding theorem is proved for the multiplex coding of bit commitment based on a noisy channel, and it is shown that several mutually independent secrets can be committed at the same time via a nosiy channel attaining the perfect secrecy of each secret with the total coding rate log \X\, where \X\ is the cardinality of channel input alphabet.