Measurement-induced deterministic and probabilistic entanglement with strong and weak interactions

A scheme is proposed to transform spatial coherence of a single particle into entanglement. Two quantum systems can be entangled by having them interact in parallel with an ancillary particle in a Mach-Zehnder interferometer, then making a suitable post-selection of the particle followed by a conditional feedforward on one of the systems to be entangled. For a strong interaction between each system and the ancilla, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state. It is demonstrated that the process is optimal when the two interactions are symmetric, systems with continuous variables are considered, and the effects of the environment are taken into account.