Global Heisenberg scaling in noisy and practical phase estimation
Bibliographic record
Abstract
Abstract Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we present a comprehensive and rigorous study of the attainability of strong, global notions of Heisenberg scaling (in contrast to the commonly studied local estimation based on e.g. quantum Fisher information) in the fundamental problem of quantum metrology, in noisy environments. As our first contribution, we formally define two useful notions of Heisenberg scaling in global estimation respectively based on the average estimation error and the limiting distribution of estimation error (which we highlight as a practically important figure of merit). A main result of this work is that for the standard phase damping noise, an O ( n −1 ) noise rate is a necessary and sufficient condition for attaining global Heisenberg scaling. We first prove that O ( n −1 ) is an upper bound on the noise rate for Heisenberg scaling to be possible, and then show by constructing a ‘robust’ estimation procedure that global Heisenberg scaling in both senses can indeed be achieved under Θ( n −1 ) noise. In addition, we provide a practically more friendly adaptive protocol using only an one-qubit memory, which achieves global Heisenberg scaling in terms of limiting distribution as well under O ( n −1 ) noise.
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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 | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".