Abstract
Quantum key distribution can provide information-theoretic security keys. In practice, the eavesdropper may attack the transmitted quantum state, which makes some information leakage to the generated key. The security of the final key depends on how difficult it is for the eavesdropper to guess the key. The guessing probability is bounded by the trace distance between the practical generated quantum state and the ideal quantum state and hence can be applied to estimate security of quantum key distribution. With the trace distance \(\varepsilon \) and the secret key length n, we prove that the guessing probability can reach the upper bound \(\varepsilon +2^{-n}\) in some special cases. We show that different attacking strategies will give different numbers of guesses, sometimes even completely subversive differences, to get the final key. Our results demonstrate that the appropriate security parameter \(\varepsilon \) should be carefully selected to guarantee the security of the generated key.
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The data that support the findings of this study are available from the corresponding authors on request.
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Acknowledgements
The author would like to thank Yan-Bao Zhang, Christopher Portmann, Marcin Pawlowski, Rong Wang and Zhen-Qiang Yin for their helpful discussions. This work is supported by the National Natural Science Foundation of China (Grant No. U2130205), the National Key Research and Development Program of China (Grant No. 2020YFA0309702) and the Natural Science Foundation of Henan (Grant No. 202300410532).
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Li, HW., Shi, JH., Cai, QY. et al. Estimating security of the quantum key distribution from the guesswork. Quantum Inf Process 21, 142 (2022). https://doi.org/10.1007/s11128-022-03487-9
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DOI: https://doi.org/10.1007/s11128-022-03487-9