Maximum Entropy Methods for Quantum State Compatibility Problems
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Bibliographic record
Abstract
Abstract Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state compatibility problem asks whether there exists a density matrix compatible with some given measurement results. Such a compatibility problem can be naturally formulated as a semidefinite programming (SDP), which searches directly for the existence of a . However, for large system dimensions, it is hard to represent directly, since it requires too many parameters. In this work, MaxEnt is applied to solve various quantum state compatibility problems, including the quantum marginal problem. An immediate advantage of the MaxEnt method is that it only needs to represent via a relatively small number of parameters, which is exactly the number of the operators measured. Furthermore, in case of incompatible measurement results, the method will further return a witness that is a supporting hyperplane of the compatible set. The method has a clear geometric meaning and can be computed effectively with hybrid quantum‐classical algorithms.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 it