A Bayesian approach to compatibility, improvement, and pooling of quantum states
Bibliographic record
Abstract
In approaches to quantum theory in which the quantum state is regarded as a representation of knowledge, information, or belief, two agents can assign different states to the same quantum system. This raises two questions: when are such state assignments compatible? and how should the state assignments of different agents be reconciled? In this paper, we address these questions from the perspective of the recently developed conditional states formalism for quantum theory [1]. Specifically, we derive a compatibility criterion proposed by Brun, Finkelstein and Mermin from the requirement that, upon acquiring data, agents should update their states using a quantum generalization of Bayesian conditioning. We provide two alternative arguments for this criterion, based on the objective and subjective Bayesian interpretations of probability theory. We then apply the same methodology to the problem of quantum state improvement, i.e. how to update your state when you learn someone else’s state assignment, and to quantum state pooling, i.e. how to combine the state assignments of several agents into a single assignment that accurately represents the views of the group. In particular, we derive a pooling rule previously proposed by Spekkens and Wiseman under much weaker assumptions than those made in the original derivation. All of our results apply to a much broader class of experimental scenarios than have been considered previously in this context.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".