We find a sufficient condition to imprint the single-mode bosonic phase-space
nonclassicality onto a bipartite state as modal entanglement and vice versa
using an arbitrary beam splitter. Surprisingly, the entanglement produced or
detected in this way depends only on the nonclassicality of the marginal input
or output states, regardless of their purity and separability. In this way, our
result provides a sufficient condition for generating entangled states of
arbitrary high temperature and arbitrary large number of particles. We also
study the evolution of the entanglement within a lossy Mach-Zehnder
interferometer and show that unless both modes are totally lost, the
entanglement does not diminish.Comment: Closest to the published version: some typos are fixed, some
references have been added, and proofs are extended a little bi
