Bibliographic record
Abstract
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the Holevo Cramér-Rao bound, suffer from multiple difficulties toward practical applicability, as the optimal measurement strategies are usually state-dependent, difficult to implement and also take complex analyses to determine. Here we study randomized measurements as an approach for multiparameter quantum metrology. We show quantum measurements on single copies of quantum states given by 3 -designs perform near-optimally when estimating an arbitrary number of parameters in pure states and more generally, approximately low-rank well-conditioned states, whose metrological information is largely concentrated in a low-dimensional subspace. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well conditioned on their supports. Examples of fidelity estimation and Hamiltonian estimation are explicitly provided to demonstrate the power and limitation of randomized measurements in multiparameter quantum metrology.
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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 | 0.006 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".