Entanglement swapping and teleportation using Mach–Zehnder interferometer assisted with a cross-Kerr cell: generation of tripartite entangled state

Abstract

In this paper, we outline new implementations for entanglement swapping and quantum teleportation using the Mach–Zehnder interferometer, where an external mode is coupled to an internal mode of the interferometer through a nonlinear cross-Kerr cell in the absence of losses and noises. The initial state of the total system contains two distinctly atom–field entangled states $$((AF)_{1,2})$$ , each previously generated via the Jaynes–Cummings model, besides an ancillary a-mode as the external mode of the Mach–Zehnder interferometer. Injecting the two-field states and a-mode into the Mach–Zehnder interferometer and then detecting both fields, the subset including the a-mode and the two atoms forms a tripartite entangled state. Therefore, entanglement swapping from $$(AF)_{1,2}$$ to the subsystem of two atoms and a-mode is appropriately performed. Next, we calculate success probability and fidelity. It is demonstrated that the maximum values of fidelity is achieved for the intensities of coherent field larger than 2. Finally, we show that the Mach–Zehnder interferometer may be used to teleport an entangled state with complete fidelity, by applying a quantum channel with an unknown state. The complete fidelity can be obtained by assuming that the dissipative factors are ignorable in the applied setups.