On the problem of non-zero word error rates for fixed-rate error correction codes in continuous variable quantum key distribution

The maximum operational range of continuous variable quantum key distribution protocols has shown to be improved by employing high-efficiency forward error correction codes. Typically, the secret key rate model for such protocols is modified to account for the non-zero word error rate of such codes. In this paper, we demonstrate that this model is incorrect: firstly, we show by example that fixed-rate error correction codes, as currently defined, can exhibit efficiencies greater than unity. Secondly, we show that using this secret key model combined with greater than unity efficiency codes, implies that it is possible to achieve a positive secret key over an entanglement breaking channel - an impossible scenario. We then consider the secret key model from a post-selection perspective, and examine the implications for key rate if we constrain the forward error correction codes to operate at low word error rates.