Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
Bibliographic record
Abstract
Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device-independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".