Noiseless attack and counterfactual security of quantum key distribution

Counterfactual quantum key distribution (QKD) enables two parties to share a secret key using an interaction-free measurement. Here, we point out that the efficiency of counterfactual QKD protocols can be enhanced by including non-counterfactual bits. This inclusion potentially gives rise to the possibility of noiseless attacks, in which Eve can gain knowledge of the key bits without introducing any errors in the quantum channel. We show how this problem can be resolved in a simple way that naturally leads to the idea of counterfactual security, whereby the non-counterfactual key bits are indicated to be secure by counterfactual detections. This method of enhancing the key rate is shown to be applicable to various existing quantum counterfactual key distribution protocols, increasing their efficiency without weakening their security.