Quantum Miniatures: quantum-like theories with limited sets of observables
Bibliographic record
Abstract
A framework is introduced for constructing models – called quantum miniatures – which structurally resemble standard quantum systems. To construct quantum miniatures, we consider an ordinary quantum system but restrict the set of physical observables, in order to examine the implications of the commonly made assumption that all self-adjoint operators represent observables. We investigate various consequences of placing a restriction on observables, which allows for a natural extension of the state space of a miniature beyond the usual quantum states. Models are developed which maximally violate uncertainty relations both for spin variables and for position and momentum, allowing for simultaneous sharp prediction of non-commuting observables. Another model exhibits postquantum non-locality, including PR box correlations. The quantum miniature framework includes standard quantum theory as a special case, and allows us to define consistent foil theories to quantum theory, including providing an explicit physical setting for a well-known family of GPTs, the polygon models of Janotta et al.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".