dorsal/arxiv
View SchemaReliability of Calderbank-Shor-Steane Codes and Security of Quantum Key Distribution
| Authors | Mitsuru Hamada |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308029 |
| URL | https://arxiv.org/abs/quant-ph/0308029 |
| DOI | 10.1088/0305-4470/37/34/009 |
| Journal | Journal of Physics A: Mathematical and General, vol.37, no.34, pp.8303--8328, Aug. 2004 |
Abstract
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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"abstract": "After Mayers (1996, 2001) gave a proof of the security of the\nBennett-Brassard 1984 (BB84) quantum key distribution protocol, Shor and\nPreskill (2000) made a remarkable observation that a Calderbank-Shor-Steane\n(CSS) code had been implicitly used in the BB84 protocol, and suggested its\nsecurity could be proven by bounding the fidelity, say F(n), of the\nincorporated CSS code of length n in the form 1-F(n) \u003c= exp[-n E+o(n)] for some\npositive number E. This work presents such a number E=E(R) as a function of the\nrate of a code R, and a threshold R\u0027 such that E(R)\u003e0 whenever R \u003c R\u0027, which is\nlarger than the achievable rate based on the Gilbert-Varshamov bound that is\nessentially due to Shor and Preskill (2000). The codes in the present work are\nrobust against fluctuations of channel parameters, which fact is needed to\nestablish the security rigorously and was not proved for rates above the\nGilbert-Varshamov rate before in the literature. As a byproduct, the security\nof a modified BB84 protocol against any joint (coherent) attacks is proved\nquantitatively.",
"arxiv_id": "quant-ph/0308029",
"authors": [
"Mitsuru Hamada"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/34/009",
"journal_ref": "Journal of Physics A: Mathematical and General, vol.37, no.34,\n pp.8303--8328, Aug. 2004",
"title": "Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key Distribution",
"url": "https://arxiv.org/abs/quant-ph/0308029"
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