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 a typical QKD protocol 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 trade-off between the secret key rate and the accuracy of parameter estimation in the finite-size regime. Here we show that continuous-variable QKD is not subject to this constraint as 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 a MDI protocol the correlations between Alice and Bob are postselected 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.