Hierarchy of multipartite correlations based on concentratable entanglement

Open Access

Hierarchy of multipartite correlations based on concentratable entanglement

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

Phys. Rev. Research 6, 023019 – Published 4 April 2024

Abstract

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.

Received 30 October 2023
Revised 13 February 2024
Accepted 15 February 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.023019

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Entanglement measures Quantum error correction Quantum formalism

Quantum Information, Science & Technology

Authors & Affiliations

Louis Schatzki ^*

Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; Illinois Quantum Information Science and Technology (IQUIST) Center, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA; and Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Guangkuo Liu

JILA, University of Colorado/NIST, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder CO 80309, USA

M. Cerezo

Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Quantum Science Center, Oak Ridge, Tennessee 37931, USA

Eric Chitambar ^†

Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA and Illinois Quantum Information Science and Technology (IQUIST) Center, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA