Relativistic quantum-speed limit for Gaussian systems and prospective experimental verification
<p dir="ltr">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...
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2025
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| Summary: | <p dir="ltr">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 − <i>p</i><sup><em>4</em></sup><i> </i>/ ( 8<i>m</i><sup><em>3</em></sup><i> c</i><sup><em>2</em></sup> ) 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 <i>ϵ</i><sup><em>2</em></sup><i> t</i><sup><em>2</em></sup> phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ( ϵ ≈ 1.5 × 10<sup>−10 </sup>) 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.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Physics Letters A<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.physleta.2025.131147" target="_blank">https://dx.doi.org/10.1016/j.physleta.2025.131147</a></p> |
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