Interaction-free generation of entanglement

In this paper, we study the generation of entanglement by interaction-free measurements. Using Kwiat 's interferometer, we construct a two-qubit quantum gate that changes one particle's trajectory according to the other particle's trajectory. We propose methods for generating the Bell state from an electron and a positron and from a pair of photons using this gate. We also show that, by using this gate, we can carry out the Bell measurement with a probability of 3/4 at the maximum and execute a controlled-NOT operation by the method proposed by Gottesman and Chuang with a probability of 9/16 at the maximum. We estimate the success probability for generating the Bell state by our procedure under imperfect interaction.