Realization of arbitrary discrete unitary transformations using spatial and internal modes of light
Bibliographic record
Abstract
Any lossless transformation on ${n}_{s}$ spatial and ${n}_{p}$ internal modes of light can be described by an ${n}_{s}{n}_{p}\ifmmode\times\else\texttimes\fi{}{n}_{s}{n}_{p}$ unitary matrix, but there is no known procedure to effect an arbitrary ${n}_{s}{n}_{p}\ifmmode\times\else\texttimes\fi{}{n}_{s}{n}_{p}$ unitary matrix on light in ${n}_{s}$ spatial and ${n}_{p}$ internal modes. We devise an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. Our realization uses beam splitters and operations on internal modes to effect arbitrary linear transformations. The number of beam splitters required to realize a unitary transformation is reduced as compared to existing realization by a factor ${n}_{p}^{2}/2$ at the cost of increasing the number of internal optical elements by a factor of 2. Our algorithm thus enables the optical implementation of higher dimensional unitary transformations.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".