Counterfactual quantum protocols for dialogue, teleportation, and comparison

Counterfactual quantum communication enables communication between remote parties without transmitting any information-carrying particle. In this paper, we propose four protocols for secure quantum communication networks utilizing such communication. The first protocol, counterfactual quantum secure direct communication (CQSDC), enables a sender to securely and counterfactually communicate a secret message. The second protocol, counterfactual quantum secure dialogue (CQSD), allows legitimate parties to transmit secret messages in each direction simultaneously, securely and counterfactually. The third protocol, counterfactual controlled quantum teleportation (CCQT), facilitates a sender to counterfactually teleport a quantum state to a receiver under the supervision of a controller. Finally, the fourth protocol, counterfactual quantum private comparison (CQPC), capacitates a third party to compare the private states of the end parties without the actual knowledge of the counterfactually transmitted states. We devise the CQSDC and CQSD protocols by exploiting the counterfactual Swap, dual chained quantum Zeno (CQZ), and distributed controlled NOT gates. For CCQT and CQPC protocols, we utilize CQZ gates with a horizontally polarized photon input. We show that the security of CQSDC and CQSD relies on counterfactual entanglement swapping, while that of CCQT and CQPC depends on establishing secure counterfactual communication channels and security validation with decoy particles, respectively.