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.

Quantum Byzantine fault tolerance (BFT) consensus is a secure and reliable mechanism that enables network nodes to reach an agreement even in the presence of faulty nodes, by using distributed private correlated lists. It plays a crucial role in developing the blockchain-based Metaverse to ensure its integrity and security. In this paper, we propose a counterfactual quantum BFT (CQ-BFT) protocol for a multipartite network using counterfactual unitary telecomputation with the chained quantum Zeno gates. This consensus protocol achieves an agreement among the parties without the passage of any physical particles through the quantum channel. Due to the unique properties of counterfactual communication, we demonstrate that the CQ-BFT protocol can operate in the absence of a shared phase reference and provide a quantum layer of security and robustness against dephasing noise, fulfilling the stringent requirements of blockchain technology. In addition, we analyze the performance tradeoff of the CQ-BFT protocol in terms of the three pillars of blockchain—i.e., security, scalability, and decentralization. The human-centric Metaverse could leverage high degrees of security, noise resilience, and fault tolerance of the CQ-BFT protocol to enhance its underlying network infrastructure. This protocol leads to more robust and immersive virtual environments that prioritize the needs and experiences of Metaverse users.

Integrating the full-duplex capability with quantum communication potentially equips emerging wireless networks with a quantum layer of security for the stringent communication efficiency and security requirements. This paper proposes two new full-duplex quantum communication protocols to exchange classical or quantum information between two remote parties simultaneously without transferring a physical particle over the quantum channel. The first protocol, called quantum duplex coding, enables the exchange of a classical bit using a preshared maximally entangled pair of qubits by means of counterfactual disentanglement. The second protocol, called quantum telexchanging, enables the exchange of an arbitrary unknown qubit without using preshared entanglement by means of counterfactual entanglement and disentanglement. We demonstrate that quantum duplex coding and quantum telexchanging can be achieved by exploiting counterfactual electron-photon interaction gates. It is shown that these tasks can be viewed as full-duplex transmission of bits and qubits via binary erasure channels and quantum erasure channels, respectively.

Distributed learning and multi-tier computing are the key ingredients to ensure ultra-reliable and low-latency communication (URLLC) in 6G networks. The distinct transition from connected things in 5G URLLC networks to connected intelligence in 6G URLLC networks requires ultra-secure communication due to the massive amount of private data. However, it is a challenging task to ensure stringent 6G URLLC requirements along with user privacy and data security in distributed networks. In this paper, we devise a distributed quantum computation protocol to perform a nonlocal controlled unitary operation on a bipartite input state in concealed and counterfactual manner and integrate it with anonymous quantum communication networks. This distributed protocol allows Bob to apply an arbitrary singlequbit unitary operator on Alice’s qubit in a controlled and probabilistic fashion, without revealing the operator to her and without transmitting any physical particle over the quantum channel-called the counterfactual concealed telecomputation (CCT). It is shown that the CCT protocol neither requires the preshared entanglement nor depends on the bipartite input state and that the single-qubit unitary teleportation is a special case of CCT. The quantum circuit for CCT can be implemented using the (chained) quantum Zeno gates. The protocol becomes deterministic with simplified circuit implementation if the initial composite state of Alice and Bob is a Bell-type state. Furthermore, we provide numerical examples of quantum anonymous broadcast networks using the CCT protocol and show their degrees of anonymity in the presence of malicious users.

In this article, an efficient numerical approach for the solution of second‐order delay differential equations to deal with the experimentation of the Internet of Industrial Things (IIoT) is presented. With the help of the Haar wavelet technique, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for various collocation points. The results show that the Haar wavelet method is an effective method for solving delay differential equations of second order. The convergence rate is also measured for various collocation points, which is almost equal to 2.