Generation and Teleportation of three and four particle W state

Abstract: In this paper, we introduced circuits for three- and four-particle quantum systems to generate W states with any arbitrary coefficients and phases. Subsequently, each qubit was transmitted separately through a four-qubit entangled channel. Before transmission, the sender performed pre-processing on their qubits to minimize the resources required for transmission. Additionally, the receiver applied post-processing using the ancilla qubit(s) to recover the final states. To further improve efficiency, it is preferable to implement the protocol in a bidirectional manner, as this allows the unknown qubits initially held by the users to be utilized ancilla qubit(s). Finally, we compared our protocol with similar works and validated the correctness of the protocol by simulating it using Qiskit, a tool provided by IBM.