Hierarchy of multipartite correlations based on concentratable entanglement

Schatzki, Louis; Liu, Guangkuo; Cerezo, M.; Chitambar, Eric

doi:10.1103/PhysRevResearch.6.023019

Title: Hierarchy of multipartite correlations based on concentratable entanglement

Journal Article · 03 April 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.023019 · OSTI ID:2333702

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Multipartite entanglement is one of the hallmarks of quantum mechanics and is central to quantum information processing. In this work we show that concentratable entanglement (CE), an operationally motivated entanglement measure, induces a hierarchy upon pure states from which different entanglement structures can be experimentally certified. In particular, we find that nearly all genuine multipartite entangled states can be verified through the CE. Interestingly, GHZ states prove to be far from maximally entangled according to this measure. Instead we find the exact maximal value and corresponding states for up to 18 qubits and show that these correspond to extremal quantum error correcting codes. The latter allows us to unravel a deep connection between CE and coding theory. Finally, our results also offer an alternative proof, on up to 31 qubits, that absolutely maximally entangled states do not exist. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

OSTI ID:: 2333702

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 6; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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