Finite-key analysis of loss-tolerant quantum key distribution based on random sampling theory

Abstract

The core of security proofs of quantum key distribution (QKD) is the estimation of a parameter that determines the amount of privacy amplification that the users need to apply in order to distill a secret key. To estimate this parameter using the observed data, one needs to apply concentration inequalities, such as random sampling theory or Azuma's inequality. The latter can be straightforwardly employed in a wider class of QKD protocols, including those that do not rely on mutually unbiased encoding bases, such as the loss-tolerant (LT) protocol. However, when applied to real-life finite-length QKD experiments, Azuma's inequality typically results in substantially lower secret-key rates. Here, we propose an alternative security analysis of the LT protocol against general attacks, for both its prepare-and-measure and measure-device-independent versions, that is based on random sampling theory. Consequently, our security proof provides considerably higher secret-key rates than the previous finite-key analysis based on Azuma's inequality. This work opens up the possibility of using random sampling theory to provide alternative security proofs for other QKD protocols.

24 pages, 5 figures. v2: Corrected a technical issue; bold math was not displayed properly in Appendix B

References in corpus (5)

• Secure Quantum Key Distribution
• Improved key rate bounds for practical decoy-state quantum key distribution systems
• Practical Quantum Key Distribution Secure Against Side-Channels
• Complementarity, distillable secret key, and distillable entanglement
• Concentration inequality using unconfirmed knowledge

Cited by in corpus (7)

• Improved Finite-Key Security Analysis of Quantum Key Distribution Against Trojan-Horse Attacks
• Preparing a commercial quantum key distribution system for certification against implementation loopholes
• Finite-key security analysis of differential-phase-shift quantum key distribution
• Security of the decoy-state BB84 protocol with imperfect state preparation
• Security framework for quantum key distribution with imperfect sources
• Numerical security analysis for quantum key distribution with partial state characterization
• Security loophole in error verification in quantum key distribution