  Despite its ubiquity in quantum computation and quantum information, a
universally applicable definition of quantum entanglement remains elusive. The
challenge is further accentuated when entanglement is associated with other key
themes, e.g., quantum interference and quantum statistics. Here, we introduce
two novel motifs that characterize the interplay of entanglement and quantum
statistics: an 'entanglement pointer' and a 'statistics-induced entanglement
entropy'. The two provide a quantitative description of the statistics-induced
entanglement: (i) they are finite only in the presence of quantum entanglement
underlined by quantum statistics; (ii) their explicit form depends on the
quantum statistics of the particles (e.g., fermions, bosons, anyons). We have
experimentally implemented these ideas by employing an electronic
Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an
integer quantum Hall platform. Performing measurements of auto-correlation and
cross-correlation of current fluctuations of the scattered beams (following
'collisions'), we quantify the statistics-induced entanglement by
experimentally accessing the entanglement pointer and the statistics-induced
entanglement entropy. Our theoretical and experimental approaches pave the way
to study entanglement in various correlated platforms, e.g., those involving
anyonic Abelian and non-Abelian states.
