Multipartite Entanglement: A Journey through Geometry
Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the “genuine” requirement, making them unsuitable for many applications. In this work, we propose a journey toward...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/26/3/217 |
| _version_ | 1797241155885203456 |
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| author | Songbo Xie Daniel Younis Yuhan Mei Joseph H. Eberly |
| author_facet | Songbo Xie Daniel Younis Yuhan Mei Joseph H. Eberly |
| author_sort | Songbo Xie |
| collection | DOAJ |
| description | Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the “genuine” requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems. |
| first_indexed | 2024-04-24T18:18:50Z |
| format | Article |
| id | doaj.art-1f97cb5a805b42b7acf82f2138323dd3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-24T18:18:50Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-1f97cb5a805b42b7acf82f2138323dd32024-03-27T13:36:52ZengMDPI AGEntropy1099-43002024-02-0126321710.3390/e26030217Multipartite Entanglement: A Journey through GeometrySongbo Xie0Daniel Younis1Yuhan Mei2Joseph H. Eberly3Center for Coherence and Quantum Optics, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USACenter for Coherence and Quantum Optics, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USACenter for Coherence and Quantum Optics, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USACenter for Coherence and Quantum Optics, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USAGenuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the “genuine” requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems.https://www.mdpi.com/1099-4300/26/3/217genuine multipartite entanglemententanglement measuregeometric measuretriangle measuretetrahedron measureentanglement entropy |
| spellingShingle | Songbo Xie Daniel Younis Yuhan Mei Joseph H. Eberly Multipartite Entanglement: A Journey through Geometry Entropy genuine multipartite entanglement entanglement measure geometric measure triangle measure tetrahedron measure entanglement entropy |
| title | Multipartite Entanglement: A Journey through Geometry |
| title_full | Multipartite Entanglement: A Journey through Geometry |
| title_fullStr | Multipartite Entanglement: A Journey through Geometry |
| title_full_unstemmed | Multipartite Entanglement: A Journey through Geometry |
| title_short | Multipartite Entanglement: A Journey through Geometry |
| title_sort | multipartite entanglement a journey through geometry |
| topic | genuine multipartite entanglement entanglement measure geometric measure triangle measure tetrahedron measure entanglement entropy |
| url | https://www.mdpi.com/1099-4300/26/3/217 |
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