Network-Irreducible Multiparty Entanglement in Quantum Matter
Bibliographic record
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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.006 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".