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

• Published in: Nature communications Vol. 15; no. 1; pp. 3428 - 8
• Main Authors: Zhang, Gu, Hong, Changki, Alkalay, Tomer, Umansky, Vladimir, Heiblum, Moty, Gornyi, Igor, Gefen, Yuval
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 23.04.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/2794; 639/766/483/481; Bosons; Cross correlation; Electron beams; Entropy; Fermions; Humanities and Social Sciences; Interferometers; multidisciplinary; Quantum computing; Quantum entanglement; Quantum phenomena; Quantum statistics; Science; Science (multidisciplinary); Statistics
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-024-47335-z

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. Measuring quantum entanglement remains a demanding task. The authors introduce two functions to quantify entanglement induced by fermionic or bosonic statistics, in transport experiments. Both functions, in theory and experiment, are remarkably resilient against the nonuniversal effects of interactions.