Analysis of counterfactuality of counterfactual communication protocols

Abstract: Counterfactual communication, i.e., communication without particle travelling in the transmission channel, is a bizarre quantum effect. Starting from interaction-free measurements many protocols achieving various tasks from counterfactual cryptogrphy to counterfactual transfer of quantum states were proposed and implemented in experiments. However, the meaning of conterfactuality in various protocols remained a controversial topic. A simple error-free counterfactual protocol is proposed. This protocol and its modification are used as a test bed for analysis of meaning of counterfactuality to clarify the counterfactuality status of various counterfactual proposals.