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arXiv · 2511.20707

Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification

Salman Sajad Wani·Aatif Kaisar Khan·Saif Al-Kuwari·Mir Faizal
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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 Cram\'er-Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an $\epsilon^{2} t^{2}$ phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ($\epsilon \approx 1.5\times 10^{-10}$) in a $5.4\,\mathrm{T}$ Penning trap, read out with $149\,\mathrm{GHz}$ quantum-limited balanced homodyne, should reveal this drift within $\sim 15\,\mathrm{min}$ -- 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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Salman Sajad Wani, Aatif Kaisar Khan, Saif Al-Kuwari, Mir Faizal. 2025-11-24. Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification. https://doi.org/10.1016/j.physleta.2025.131147

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