  In this paper, we study how to generate entanglement by interaction-free
measurement. Using Kwiat et al.'s interferometer, we construct a two-qubit
quantum gate that changes a 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 by this gate. We also show
that using this gate, we can carry out the Bell measurement with the
probability of 3/4 at the maximum and execute a controlled-NOT operation by the
method proposed by Gottesman and Chuang with the probability of 9/16 at the
maximum. We estimate the success probability for generating the Bell state by
our procedure under imperfect interaction.
