Multipartite Embezzlement of Entanglement
Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, 30167 Hannover, Germany
| Published: | 2025-07-30, volume 9, page 1818 |
| Editor: | Paul Skrzypczyk |
| Eprint: | arXiv:2409.07646v3 |
| Doi: | https://doi.org/10.22331/q-2025-07-30-1818 |
| Citation: | Quantum 9, 1818 (2025). |
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Abstract
Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via local operations and without communication while perturbing the resource arbitrarily little. Recently, the existence of embezzling states of bipartite systems of type III von Neumann algebras was shown. However, both the multipartite case and the precise relation between embezzling states and the notion of embezzling families, as originally defined by van Dam and Hayden, was left open. Here, we show that finite-dimensional approximations of multipartite embezzling states form multipartite embezzling families. In contrast, not every embezzling family converges to an embezzling state. We identify an additional consistency condition that ensures that an embezzling family converges to an embezzling state. This criterion distinguishes the embezzling family of van Dam and Hayden from the one by Leung, Toner, and Watrous. The latter generalizes to the multipartite setting. By taking a limit, we obtain a multipartite system of commuting type III$_1$ factors on which every state is an embezzling state. We discuss our results in the context of quantum field theory and quantum many-body physics. As open problems, we ask whether vacua of relativistic quantum fields in more than two spacetime dimensions are multipartite embezzling states and whether multipartite embezzlement allows for an operator-algebraic characterization.
Featured image: Left: Application to relativistic quantum field theory, where agents can use the vacuum on larger and larger, but finite systems to embezzle entanglement. Right: A two-dimensional many-body system may be subdivided into three infinite subsystems. Can the ground state of such a system be a multipartite embezzling state?
Popular summary
Only recently was it established that certain systems host infinitely entangled resource states from which arbitrary entangled states can be embezzled. Previously, only families of states with this property were known, where, to increase the accuracy of embezzlement, one needed to consider larger and larger resource systems.
This paper has two main contributions: First, it shows that embezzlement of entanglement generalizes to multipartite entanglement, i.e., entangled states shared between more than two agents. Second, it clarifies the relation between previously established embezzlement families and the recently discovered embezzling states.
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Cited by
[1] Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, and Henrik Wilming, "Pure State Entanglement and von Neumann Algebras", Communications in Mathematical Physics 406 12, 296 (2025).
[2] Kensuke Gallock-Yoshimura and Erickson Tjoa, "Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model", Physical Review D 112 8, 085024 (2025).
[3] David Pérez-García, Volume 5: Invited Lectures: Sections 9–11 534 (2026) ISBN:978-1-61197-868-1.
[4] Lauritz van Luijk, Alexander Stottmeister, and Henrik Wilming, "Critical fermions are universal embezzlers", Nature Physics 21 7, 1141 (2025).
[5] Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, and Henrik Wilming, "Relativistic Quantum Fields Are Universal Entanglement Embezzlers", Physical Review Letters 133 26, 261602 (2024).
[6] Lauritz van Luijk, Alexander Stottmeister, and Henrik Wilming, "The Large-Scale Structure of Entanglement in Quantum Many-body Systems", arXiv:2503.03833, (2025).
[7] Alessia Kera, Lauritz van Luijk, Alexander Stottmeister, and Henrik Wilming, "Gaussian fermionic embezzlement of entanglement", arXiv:2509.15749, (2025).
[8] Tal Schwartzman, "Complexity of entanglement embezzlement", Physical Review A 112 1, 012415 (2025).
[9] Lauritz van Luijk, "Entanglement in von Neumann Algebraic Quantum Information Theory", arXiv:2510.07563, (2025).
[10] Kristin Courtney, Niklas Galke, Lauritz van Luijk, and Alexander Stottmeister, "Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem", arXiv:2510.02019, (2025).
[11] Li Liu, "Explicit C*-algebraic Protocol for Exact Universal Embezzlement of Entanglement", arXiv:2506.10736, (2025).
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