Measuring statistics-induced entanglement entropy with a Hong–Ou–Mandel interferometer

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 and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions,
bosons, and anyons). We have experimentally implemented these ideas by mploying 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 fluctua-
tions of the scattered beams (following ‘collisions’), we quantify the statisticsinduced entanglement by experimentally accessing the entanglement pointer
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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.