Information reconciliation for discretely-modulated continuous-variable quantum key distribution

The goal of this note is to explain the reconciliation problem for continuous-variable quantum key distribution protocols with a discrete modulation. Such modulation formats are attractive since they significantly simplify experimental implementations compared to protocols with a Gaussian modulation. Previous security proofs that relied crucially on the Gaussian distribution of the input states are rendered inapplicable, and new proofs based on the entropy accumulation theorem have emerged. Unfortunately, these proofs are not compatible with existing reconciliation procedures, and necessitate a reevaluation of the reconciliation problem. We argue that this problem is nontrivial and deserves further attention. In particular, assuming it can be solved with optimal efficiency leads to overly optimistic predictions for the performance of the key distribution protocol, in particular for long distances.