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Multipartite Entanglement: A Journey through Geometry.

Songbo Xie1, Daniel Younis1, Yuhan Mei1

  • 1Center for Coherence and Quantum Optics, Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA.

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Summary
This summary is machine-generated.

Quantifying genuine multipartite entanglement is challenging. This study introduces a novel tetrahedron measure for quadripartite entanglement, linking it to geometric hypervolumes and permutation invariance for quantum information applications.

Keywords:
entanglement entropyentanglement measureentanglement polygon inequalitiesentropic fillgenuine multipartite entanglementgeometric measureinformation scramblingpermutation invariancetetrahedron measuretriangle measure

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Many-Body Systems

Background:

  • Genuine multipartite entanglement is essential for quantum information processing and technologies.
  • Existing entanglement measures often fail to satisfy the 'genuine' requirement, limiting their applicability.
  • Quantifying multipartite entanglement remains a significant challenge in quantum physics.

Purpose of the Study:

  • To introduce a novel and robust measure for quantifying genuine quadripartite entanglement.
  • To establish a connection between multipartite entanglement and geometric properties of quantum states.
  • To explore the potential applications of the proposed measure in quantum information scrambling.

Main Methods:

  • Development of a 'tetrahedron measure' based on the hypervolume of geometric simplices.
  • Analysis of the relationship between the proposed measure and permutation invariance among quantum system parties.
  • Comparison of entanglement rankings for highly entangled four-qubit states using the new measure.

Main Results:

  • A novel tetrahedron measure for quadripartite entanglement is proposed.
  • The measure demonstrates a dependence on the degree of permutation invariance within the quantum system.
  • The study reveals an unexpected link between multipartite entanglement and geometric hypervolumes.

Conclusions:

  • The proposed tetrahedron measure offers a promising approach to quantifying genuine quadripartite entanglement.
  • This work provides new insights into the geometric nature of multipartite entanglement.
  • The measure has potential applications in understanding quantum information scrambling in complex quantum systems.