Realization of the Einstein-Podolsky-Rosen Paradox Using Radial Position and Radial Momentum Variables
Bibliographic record
Abstract
As is well known, angular position and orbital angular momentum (OAM) of photons are a conjugate pair of variables that have been extensively explored for quantum information science and technology. In contrast, the radial degrees of freedom remain relatively unexplored. Here we exploit the radial variables, i.e., radial position and radial momentum, to demonstrate Einstein-Podolsky-Rosen correlations between down-converted photons. In our experiment, we prepare various annular apertures to define the radial positions and use eigenmode projection to measure the radial momenta. The resulting correlations are found to violate the Heisenberg-like uncertainty principle for independent particles, thus manifesting the entangled feature in the radial structure of two-photon wave functions. Our work suggests that, in parallel with angular position and OAM, the radial position and radial momentum can offer a new platform for a fundamental test of quantum mechanics and for novel application of quantum information.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".