Security Bounds for Efficient Decoy-State Quantum Key Distribution

Marco Lucamarini, James F. Dynes, Bernd Fröhlich, Zhiliang Yuan, Andrew J. Shields

Research output: Contribution to journalReview articlepeer-review


Information-theoretical security of quantum key distribution (QKD) has been convincingly proven in recent years and remarkable experiments have shown the potential of QKD for real-world applications. Due to its unique capability of combining high key rate and security in a realistic finite-size scenario, the efficient version of the BB84 QKD protocol endowed with decoy states has been subject of intensive research. Its recent experimental implementation finally demonstrated a secure key rate beyond 1 Mb/s over a 50 km of optical fiber. However, the achieved rate holds under the restrictive assumption that the eavesdropper performs collective attacks. Here, we review the protocol and generalize its security. We exploit a map by Ahrens to rigorously upper bound the hypergeometric distribution resulting from a general eavesdropping. Despite the extended applicability of the new protocol, its key rate is only marginally smaller than its predecessor in all cases of practical interest.

Original languageEnglish
Article number7021899
Pages (from-to)197-204
Number of pages8
JournalIEEE Journal of Selected Topics in Quantum Electronics
Issue number3
Publication statusPublished - 1 May 2015


  • BB84 protocol
  • collective attacks
  • confidence interval
  • finite-size effects
  • independent identically distributed random variable
  • Quantum communications
  • quantum key distribution
  • sampling theory

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