Separable ellipsoids around multipartite states
Bibliographic record
Abstract
We show that, in finite dimensions, around any $m$-partite product state $ρ_{\rm prod}=ρ_1\otimes...\otimesρ_m$, there exists an ellipsoid of separable states centered around $ρ_{\rm prod}$. This separable ellipsoid contains the separable ball proposed in previous works, and the volume of the ellipsoid is typically exponentially larger than that of the ball, due to the hierarchy of eigenvalues in typical states. We further generalize this ellipsoidal criterion to a trace formula that yields separable region around all separable states, and further study biseparability. Our criteria not only help numerical procedures to rigorously detect separability, but they also lead to a nested hierarchy of SLOCC-stable subsets that cover the separable set. We apply the procedure for separability detection to 3-qubit X states, genuinely entangled 4-qubit states mixed with noise, and the 1d transverse field Ising model at finite temperature to illustrate the power of our procedure for understanding entanglement in physical systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.003 |
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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".