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arXiv:2512.11118 · Physical Review Letters

Network-Irreducible Multiparty Entanglement in Quantum Matter

Liuke Lyu, Pedro Lauand, William Witczak-Krempa

quant-phcond-mat.str-elhep-thSubmitted Dec 11, 2025• Announced Dec 15, 2025• 0 citations
v1 · Dec 11, 2025v2 · Apr 27, 2026
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Abstract

We show that the standard approach to characterize collective entanglement via genuine multiparty entanglement (GME) leads to an area law in ground and thermal Gibbs states of local Hamiltonians. To capture the truly collective part one needs to go beyond this short-range contribution tied to interfaces between subregions. Genuine network multiparty entanglement (GNME) achieves a systematic resolution of this goal by analyzing whether a $k$-party state can be prepared by a quantum network consisting of $(k-1)$-partite resources. We develop tools to certify and quantify GNME, and benchmark them for GHZ, W and Dicke states. We then study the 1d transverse field Ising model, where we find a sharp peak of GNME near the critical phase transition, and rapid suppression elsewhere. Finite temperature leads to a faster death of GNME compared to GME. Furthermore, certain 2d quantum spin liquids do not have GNME in microscopic subregions while possessing strong GME. This approach will allow to chart truly collective entanglement in quantum matter both in and out of equilibrium.

Journal reference
Phys. Rev. Lett. 137, 110204 (2026)
DOI
10.1103/jv51-thxz
Comments
20 pages, 14 figures

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We show that the standard approach to characterize collective entanglement via genuine multiparty entanglement (GME) leads to an area law in ground and thermal Gibbs states of local Hamiltonians. To capture the truly collective part one needs to go beyond this short-range contribution tied to interfaces between subregions. Genuine network multiparty entanglement (GNME) achieves a systematic resolution of this goal by analyzing whether a kkk-party state can be prepared by a quantum network consisting of (k−1)(k-1)(k−1)-partite resources. We develop tools to certify and quantify GNME, and benchmark them for GHZ, W and Dicke states. We then study the 1d transverse field Ising model, where we find a sharp peak of GNME near the critical phase transition, and rapid suppression elsewhere. Finite temperature leads to a faster death of GNME compared to GME. Furthermore, certain 2d quantum spin liquids do not have GNME in microscopic subregions while possessing strong GME. This approach will allow to chart truly collective entanglement in quantum matter both in and out of equilibrium.
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Abstract Quantum spin liquids (QSLs) give rise to exotic emergent particles by weaving intricate entanglement patterns in the underlying electrons. Bipartite measures between subregions can detect the presence of anyons, but little is known about the full entanglement structure of QSLs. Here, we study the multiparty entanglement of QSLs via entanglement microscopy. We find that in contrast to conventional matter, the genuine multiparty entanglement (GME) between spins is absent in the smallest subregions, a phenomenon we call ``entanglement frustration.'' Instead, GME is more collective, and arises solely in loops. By exploiting exact results and large-scale numerics, we confirm these properties in various gapped and gapless QSLs realized in physically motivated Hamiltonians, as well as with string-net wavefunctions hosting abelian or non-abelian anyons. Our results shed new light on the phase diagram of Kitaev’s honeycomb model in a Zeeman field, and the Kagome Heisenberg model under various perturbations. Going beyond QSLs, we provide evidence that entanglement loops are a universal property of quantum gauge theories. This leads to a new understanding of fractionalization, and the means by which gauge bosons encode quantum information.
Quantifying multipartite entanglement in quantum many-body systems and hybrid quantum computing architectures is a fundamental yet challenging task. In recent years, thermodynamic quantities such as the maximum extractable work from an isolated system (the ergotropy) have allowed for entanglement measures that are operationally more accessible. However, these measures can be restrictive when applied to systems governed by Hamiltonians with strong collective or interparticle interactions. Motivated by advances in quantum simulators, we propose a framework that circumvents these restrictions by evaluating global and local ergotropy either through controlled quenching of interactions or by measuring suitable local observables only. We show that this formalism allows us to correctly estimate genuine multipartite entanglement in both stationary and time-evolved states of systems with strong interactions, including parametrized quantum states simulated on a quantum circuit with varying circuit depth and noise. We demonstrate its applicability to realistic physical models, namely, the Tavis-Cummings model, the three-level Dicke model, and the transverse-field Ising model, highlighting its potential as a versatile tool for characterizing entanglement in near-term quantum simulators.
Quantum entanglement uncovers the essential principles of quantum matter, yet determining its structure in realistic many-body systems poses significant challenges. Here, we employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of the microscopic subregion in spin and fermionic many-body systems. We exemplify our method by studying the phase diagram near quantum critical points (QCP) in 2 spatial dimensions: the transverse field Ising model and a Gross-Neveu-Yukawa transition of Dirac fermions. Our main results are: i) the Ising QCP exhibits short-range entanglement with a finite sudden death of the LN both in space and temperature; ii) the Gross-Neveu QCP has a power-law decaying fermionic LN consistent with conformal field theory (CFT) exponents; iii) going beyond bipartite entanglement, we find no detectable 3-party entanglement with our two witnesses in a large parameter window near the Ising QCP in 2d, in contrast to 1d. We further establish the singular scaling of general multipartite entanglement measures at criticality and present an explicit analysis in the tripartite case. Quantum entanglement contains important information about quantum systems, but its calculation is challenging. Here the authors develop a quantum Monte Carlo technique for full tomography on microscopic subregions of a system, enabling extraction of multipartite quantum entanglement in large scale models.
We establish operational limits on the broadcasting of genuine multipartite entanglement (GME) in quantum networks. Using a distributed protocol in which each of N parties locally implements optimal 1 →\to→ 2 cloning via beam-splitter interactions, we derive exact expressions for the broadcast fidelity of Greenberger-Horne-Zeilinger (GHZ), W states, and Cluster states in a limited setting. We show that the fidelity decays exponentially with system size as [c(R)]N^NN, providing a quantitative expression of multipartite entanglement monogamy in the broadcasting setting, and that both state families share a universal normalisation factor arising from independent post-selection probabilities. Most significantly, we prove a no-go result for simultaneous GME certification: for all reflectivities and all system sizes, the two broadcast copies cannot be simultaneously certified as genuinely multipartite entangled within the standard framework of fidelity-based witnesses. We further check this behaviour for three- and four-party cluster states, finding consistent results that support the generality of the no-go beyond the GHZ and W families. This obstruction arises from the redistribution of multipartite coherence, which both reduces the achievable fidelity and increases the corresponding certification threshold. Our results reveal a fundamental trade-off between the broadcastability of multipartite entanglement and its operational certifiability, and delineate intrinsic limits on entanglement distribution in quantum networks.
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