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arXiv · 2207.07584

Experimental Examination of Entanglement Estimates

Songbo Xie·Yuan-Yuan Zhao·Chao Zhang·Yun-Feng Huang·Chuan-Feng Li·Guang-Can Guo·Joseph H. Eberly
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Abstract

Recently a proper genuine multipartite entanglement (GME) measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)], but capturing useful entanglement measures for mixed states has remained an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by Gühne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of {\em any} Hermitian operator. Moreover, we identify a class of operators $\A_1$ which not only give good estimates, but also require a remarkably small number of experimental measurements. In this note we define our approach and illustrate it by estimating entanglement measures for a number of pure and mixed states prepared in our recent experiments.

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Songbo Xie, Yuan-Yuan Zhao, Chao Zhang, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Joseph H. Eberly. 2023-04-12. Experimental Examination of Entanglement Estimates. https://doi.org/10.1103/physrevlett.130.150801

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