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The security of quantum key distribution protocols is guaranteed by the lawsof quantum mechanics. However, a precise analysis of the security propertiesrequires tools from both classical cryptography and information theory. Here,we employ recent results in non-asymptotic classical information theory to showthat one-way information reconciliation imposes fundamental limitations on theamount of secret key that can be extracted in the finite key regime. Inparticular, we find that an often used approximation for the informationleakage during information reconciliation is not generally valid. We propose animproved approximation that takes into account finite key effects andnumerically test it against codes for two probability distributions, that wecall binary-binary and binary-Gaussian, that typically appear in quantum keydistribution protocols.

Fundamental Finite Key Limits for One-Way Information Reconciliation in Quantum Key Distribution