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

Gu Zhang, Changki Hong, Tomer Alkalay, Vladimir Umansky, Moty Heiblum (), Igor Gornyi () and Yuval Gefen ()
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Gu Zhang: Beijing Academy of Quantum Information Sciences
Changki Hong: Weizmann Institute of Science
Tomer Alkalay: Weizmann Institute of Science
Vladimir Umansky: Weizmann Institute of Science
Moty Heiblum: Weizmann Institute of Science
Igor Gornyi: Karlsruhe Institute of Technology
Yuval Gefen: Weizmann Institute of Science

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: Abstract 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 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.

Date: 2024
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DOI: 10.1038/s41467-024-47335-z

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