Entanglement monotones for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-type states
Bibliographic record
Abstract
In this article, we extend recent results concerning random-pair Einstein-Podolsky-Rosen distillation and the operational gap between separable operations (SEPs) and local operations with classical communication (LOCC). In particular, we consider the problem of obtaining bipartite maximal entanglement from an $N$-qubit $W$-class state (i.e., that of the form $\sqrt{{x}_{0}}|00\ensuremath{\cdots}0\ensuremath{\rangle}+\sqrt{{x}_{1}}|10\ensuremath{\cdots}0\ensuremath{\rangle}+\ensuremath{\cdots}+\sqrt{{x}_{n}}|00\ensuremath{\cdots}1\ensuremath{\rangle}$) when the target pairs are a priori unspecified. We show that when ${x}_{0}=0$, the optimal probabilities for SEPs can be computed using semidefinite programming. On the other hand, to bound the optimal probabilities achievable by LOCC, we introduce entanglement monotones defined on the $N$-qubit $W$ class of states. The LOCC monotones we construct can be increased by SEPs, and in terms of transformation success probability, we are able to quantify a gap as large as 37$%$ between the two classes. Additionally, we demonstrate transformations ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}n}\ensuremath{\rightarrow}{\ensuremath{\sigma}}^{\ensuremath{\bigotimes}n}$ that are feasible by SEP for any $n$ but impossible by LOCC.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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 teacher head, 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".