Quantum theories with alternative measurement postulates
Bibliographic record
Abstract
Two measurements of an observable always yield identical outcomes when implemented in quick succession on a quantum system. In the standard formulation of non-relativistic quantum theory, this phenomenon is accounted for by the collapse of the state induced by a non-destructive measurement. In the first part of this thesis, we investigate the role of the collapse in quantum theory in a systematic way. We introduce the framework of Alternative-Measurement Theories (AMTs) defined as no-signalling foils of quantum mechanics sharing with it all standard postulates, except for the update rule assigning post-measurement states. By embedding quantum mechanics in a set of structurally similar theories, we are able to identify properties that depend on the collapse and show which of them are unique to the Lüders projection rule. We show that update rules can affect the ontological status of quantum states, or not allow for non-local correlations. The operational equivalence of different experimental strategies to measure product observables is found to rely on the chosen update rule, as well as the feasibility of protocols such as local tomography. The comparison with individual AMTs, such as "passive quantum theory" characterised by measurements which cause no state update, allows us to identify operational assumptions from which the Lüders rule can be derived. We show that the repeatability of measurement outcomes is insufficient; a stronger assumption on degenerate observables proves sufficient, at least for non-composite systems. In the second part, we focus on support uncertainty relations in spaces of prime dimensions. Tao derived a state-independent inequality which holds for the support sizes of a pure qudit state in two bases related by a discrete Fourier transform. We generalise Tao’s uncertainty relation to complete sets of (d+1) mutually unbiased bases in prime-dimensional spaces and investigate the sharpness of the obtained lower bounds.
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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 | 0.008 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.012 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| 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".