Abstract
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and most importantly, the security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is the deviation between phase error rate of computational basis and bit error rate of dual basis. Here, we provide the rigorous and optimal analytic formula to solve the above tasks, resulting to higher secret key rate and longer secure transmission distance. Our results can be widely applied to deal with statistical fluctuation in quantum cryptography protocols.
Highlights
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime
By exploiting the decoy-state method, one can establish the linear system of equations about the expected values to obtain expected value of yield of the single-photon component, where we need estimate the expected value of some parameters given by the known observed values
We proposed the almost optimal analytical formulas to deal with the statistical fluctuation under the security against the general attacks
Summary
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. The expected value of yield (bit error rate) of n-photon in signal state and decoy state are identical while the corresponding observed value cannot be assumed to be the same in the finite-key regime. By exploiting the decoy-state method, one can establish the linear system of equations about the expected values to obtain expected value of yield (bit error rate) of the single-photon component, where we need estimate the expected value of some parameters given by the known observed values. The observed value of yield (bit error rate) of the single-photon component in the key extraction data is what we really need, where we must estimate the observed value given by the known expected value. Note that the result of Gaussian analysis should be optimal because the identically distributed assumption is a special case
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