Physics – Quantum Physics
Scientific paper
2003-08-05
Journal of Physics A: Mathematical and General, vol.37, no.34, pp.8303--8328, Aug. 2004
Physics
Quantum Physics
No figure. Ver.2: Security criterion slightly refined. 25 pages. Ver.3: Completely revised to fix a serious error. The existen
Scientific paper
10.1088/0305-4470/37/34/009
After Mayers (1996, 2001) gave a proof of the security of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol, Shor and Preskill (2000) made a remarkable observation that a Calderbank-Shor-Steane (CSS) code had been implicitly used in the BB84 protocol, and suggested its security could be proven by bounding the fidelity, say F(n), of the incorporated CSS code of length n in the form 1-F(n) <= exp[-n E+o(n)] for some positive number E. This work presents such a number E=E(R) as a function of the rate of a code R, and a threshold R' such that E(R)>0 whenever R < R', which is larger than the achievable rate based on the Gilbert-Varshamov bound that is essentially due to Shor and Preskill (2000). The codes in the present work are robust against fluctuations of channel parameters, which fact is needed to establish the security rigorously and was not proved for rates above the Gilbert-Varshamov rate before in the literature. As a byproduct, the security of a modified BB84 protocol against any joint (coherent) attacks is proved quantitatively.
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