Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key
  Distribution   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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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: adap-org