Time uncertainty and fundamental sensitivity limits in quantum sensing: Application to optomechanical gravimetry
Year: 2026
Authors: Wani S.S., Al-Kuwari S., Shabir A., Vezio P., Marino F., Faizal M.
Autors Affiliation: Hamad Bin Khalifa Univ, Qatar Ctr Quantum Comp, Coll Sci & Engn, Doha, Qatar; Canadian Quantum Res Ctr, 460 Doyle Ave 106, Kelowna, BC V1Y 0C2, Canada; Univ Firenze, Dipartimento Fis Astron, Via Sansone 1, I-50019 Sesto Fiorentino, Firenze, Italy; CNR Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, Firenze, Italy; INFN, Via Sansone 1, I-50019 Sesto Fiorentino, Firenze, Italy; Univ British Columbia Okanagan, Irving K Barber Sch Arts & Sci, Kelowna, BC V1V 1V7, Canada; Univ Durham, Dept Math Sci, Stockton Rd, Durham DH1 3LE, England; Hasselt Univ, Fac Sci, Computat Math Grp, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.
Abstract: High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity, are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram & eacute;r-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.
Journal/Review: PHYSICAL REVIEW A
Volume: 113 (3) Pages from: 32609-1 to: 32609-11
KeyWords: RelativityDOI: 10.1103/nn67-9tph
