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

• URL: http://arxiv.org/abs/2511.20707v1
• Date: Mon, 24 Nov 2025 21:48:36 GMT
• Title: Relativistic Quantum-Speed Limit for Gaussian Systems and Prospective Experimental Verification
• Authors: Salman Sajad Wani, Aatif Kaisar Khan, Saif Al-Kuwari, Mir Faizal,
• Abstract summary: We derive first-order relativistic corrections to the Mandelstam-Tamm and Margolus-Levitin bounds.<n>Results point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ($ε\approx 1.5\times 10^{-10}$) 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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