From uniformity to fluctuations: Quantifying the security cost of imperfect randomness in quantum key distribution

Abstract

Quantum key distribution protocols typically assume that the random number generators driving state preparation, basis selection and classical post-processing produce perfectly uniform and statistically independent outputs, an assumption that may not be justified under realistic experimental conditions. A nonrandom choice of basis at the state-preparation or measurement stage may lead to an underestimation of the eavesdropper's accessible information. Increasing asymmetry monotonically decreases the source entropy and the Holevo information, reducing the conditional entropy and the extractable secret key length, and at deterministic preparation no secure key can be distilled. In the non-independent and identically distributed regime, characterised by signalwise fluctuations in the a priori probabilities, the reduction in conditional entropy is proportional to the second moment of the deviation distribution, and such fluctuations cannot be resolved by deterministic adjustments to the final key length.