Efficient implementation of complete and nondestructive Bell-state measurement for trapped ions with reverse engineering

In this paper, we put forward a protocol for the complete and nondestructive Bell-state measurement of trapped ions. We show that the four different Bell states of two information carriers can be distinguished using two auxiliary ions with the initial Bell states unchanged after the procedures. The parameter selections are discussed based on the experimentally available parameters, and the robustness against the errors and decoherence are analyzed. The results show that the protocol works well with the selected parameters, and possesses robustness against errors and decoherence. Since the laser pulses to drive the transitions of ions in the procedures are designed via reverse engineering, the control parameters can be flexibly selected under certain boundary conditions, which provides the possibility to find corrective parameters to compensate the errors caused by the decoherence. We hope the protocol can be useful for the Bell-state based quantum information tasks.