Multistage entanglement swapping using superconducting qubits in the absence and presence of dissipative environment without Bell state measurement

Abstract In recent decade the entangled state generation is of great importance in the quantum information processing and technologies. In this paper, producing the distributed entangled state of superconducting (SC) qubits is considered using an entanglement swapping protocol in three successive stages. The SC qubit pairs (i, i+1 with i=1, 3, 5, 7), where each pair of the qubits has been placed on a separate chip, are initially prepared in maximally entangled states. The external magnetic fields on capacitively coupled pairs (2, 3) and (6, 7) are implemented for modulating the qubits. Then, the SC qubits (1, 4) and (5, 8) are converted into entangled states via operating proper measurements instead of Bell state measurement (which is generally a hard task). Finally, the distributed entangled state of target SC qubits (1, 8) can be obtained by applying external magnetic fields on qubits (4, 5) and operating suitable measurements. This process is studied in the absence and presence of thermal decoherence effects. The concurrence, as a measure of entanglement between two qubits, success probability of the distributed entangled states and fidelity are evaluated, by which we find that the state of target SC qubits (1, 8) is converted to Bell state at some moments of time. Also, there exist appropriate conditions in which maximum of success probability of the obtained states in each stage approaches 1. Also, the maxima of concurrence and success probability gradually decrease due to thermal noise as time goes on. Moreover, convincing amounts of fidelity, success probability and entanglement can be obtained for the achieved entangled states.