Fully counterfactual quantum communication protocols within a twin-field framework

Counterfactual communication refers to cases in which information is exchanged between two remote parties without actual transmission of physical particles. We propose a fully tripartite counterfactual quantum protocol for the task of identity authentication. Here, a trusted certificate authority (Charlie) enables a client (Alice) and an entity (Bob) to share a secure random key based on the modification of early protocols by Aharonov and Vaidman, therefore permitting communication that is counterfactual according to the two-state vector formalism. The protocol has high robustness against environmental noise, while still passing the Fisher information test. With semi-honest Charlie, the counterfactual protocol transforms identity authorization into quantum-assisted key distribution. We show that the counterfactual quantum key distribution can be made secure within a twin-field framework. Our simulation results show that the maximal secure distance of the counterfactual protocol with a practical weak coherent state is around 190 km.