Parameter estimation with almost no public communication for continuous-variable quantum key distribution

One crucial step in any quantum key distribution (QKD) scheme is parameter estimation. In all known QKD protocols, if prior information is not available, the users have to sacrifice part of their raw data to estimate the parameters of the communication channel as, for example, the error rate. This introduces a tradeoff between the secret key rate and the accuracy or parameter estimation in the finite-size regime. Here we show that continuous-variable (CV) QKD is not subject to this constraint and the whole raw keys can be used for both parameter estimation and secret key generation, without compromising the security. First we show that this property holds for measurement-device independent (MDI) protocols, as a consequence of the fact that in an MDI protocol the correlations between Alice and Bob are post-selected by the measurement performed by an untrusted relay. This result is then extended beyond the MDI framework by exploiting the fact that MDI protocols can simulate device-dependent one-way QKD with arbitrarily high precision.