Relativistic quantum-speed limit for Gaussian systems and prospective experimental verification
Bibliographic record
Abstract
Timing and phase resolution in satellite QKD, kilometre-scale gravitational-wave detectors, and space-borne clock networks hinge on quantum–speed limits (QSLs), yet benchmarks omit relativistic effects for coherent and squeezed probes. We derive first-order relativistic corrections to the Mandelstam–Tamm and Margolus–Levitin bounds. Starting from the Foldy–Wouthuysen expansion and treating − p 4 / ( 8 m 3 c 2 ) as a harmonic-oscillator perturbation, we propagate Gaussian states to obtain closed-form QSLs and the quantum Cramér–Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an ϵ 2 t 2 phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ( ϵ ≈ 1.5 × 10 − 10 ) in a 5.4 T Penning trap, read out with 149 GHz quantum-limited balanced homodyne, should reveal this drift within ∼ 15 min — within known hold times. These results benchmark relativistic corrections in continuous-variable systems and point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".