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

Gu Zhang; Changki Hong; Tomer Alkalay; Vladimir Umansky; Moty Heiblum; Igor V Gornyi; Yuval Gefen

doi:10.1038/s41467-024-47335-z

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

Gu Zhang, Changki Hong, Tomer Alkalay, Vladimir Umansky, Moty Heiblum^*, Igor V Gornyi^*, Yuval Gefen^*

^*Corresponding author for this work

Department of Condensed Matter Physics

Research output: Contribution to journal › Article › peer-review

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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; (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.

Original language	English
Article number	3428
Journal	Nature Communications
Volume	15
Issue number	1
DOIs	https://doi.org/10.1038/s41467-024-47335-z
Publication status	Published - 23 Apr 2024

Bibliographical note

We acknowledge Dong E. Liu, Gabriele Campagnano, Christian Glattli, and Janine Splettstoesser for useful comments, and Yunchul Chung and Hyungkook Choi for the discussion of the experiments. I.G. and Y.G. acknowledge the support from the DFG grant No. MI658/10-2 and German-Israeli Foundation (GIF) grant No. I-1505-303.10/2019. Y.G. acknowledges support from the Helmholtz International Fellow Award, the DFG Grant RO 2247/11-1, CRC 183 (project C01), the US-Israel Binational Science Foundation, and the Minerva Foundation. M.H. acknowledges the continuous support of the Sub-Micron Center staff and the support of the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 833078).

All Science Journal Classification (ASJC) codes

General Chemistry
General Biochemistry,Genetics and Molecular Biology
General Physics and Astronomy

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mh_NatCommun_MeasuringStatisticsInduced_PV_2024Final published version, 1.1 MBLicence: CC BY

https://arxiv.org/abs/2210.15520Licence: CC BY-NC-SA

Cite this

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title = "Measuring statistics-induced entanglement entropy with a Hong–Ou–Mandel interferometer",

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; (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.",

author = "Gu Zhang and Changki Hong and Tomer Alkalay and Vladimir Umansky and Moty Heiblum and Gornyi, {Igor V} and Yuval Gefen",

note = "We acknowledge Dong E. Liu, Gabriele Campagnano, Christian Glattli, and Janine Splettstoesser for useful comments, and Yunchul Chung and Hyungkook Choi for the discussion of the experiments. I.G. and Y.G. acknowledge the support from the DFG grant No. MI658/10-2 and German-Israeli Foundation (GIF) grant No. I-1505-303.10/2019. Y.G. acknowledges support from the Helmholtz International Fellow Award, the DFG Grant RO 2247/11-1, CRC 183 (project C01), the US-Israel Binational Science Foundation, and the Minerva Foundation. M.H. acknowledges the continuous support of the Sub-Micron Center staff and the support of the European Research Council under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement number 833078).",

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N2 - 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.

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

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Bibliographical note

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