Multipartite Entanglement: A Journey Through Geometry
- URL: http://arxiv.org/abs/2304.03281v2
- Date: Mon, 5 Feb 2024 19:56:23 GMT
- Title: Multipartite Entanglement: A Journey Through Geometry
- Authors: Songbo Xie, Daniel Younis, Yuhan Mei, Joseph H. Eberly
- Abstract summary: Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge.
We introduce an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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