Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2510.00057 · Physical review. D/Physical review. D.

Quantum speed limit as a sensitive probe of Planck-scale effects

Salman Sajad Wani, Saif M. Al-Kuwari

Published Sep 11, 2025• 1 citation
arXivHTMLPDF

Abstract

Many quantum-gravity scenarios predict a minute modification of the canonical commutator, known as the generalized uncertainty principle (GUP), whose low-energy signatures are, in principle, accessible to state-of-the-art laboratory tests. We compute first-order minimal-length corrections to the quantum speed limit (QSL) for three cases: uniform superpositions in an infinite square well, coherent harmonic-oscillator states, and squeezed-oscillator states. We identify a universal amplification law: for any pure state, the fractional shift of either speed limit scales linearly with $β$ and algebraically with the state's effective Hilbert-space size. As the effective Hilbert-space dimension can be exceedingly large, the associated minimal-length signatures are amplified by several orders of magnitude. Using high-precision matter-wave timing data, we set a direct bound on the GUP parameter $β$, which quantifies minimal-length quantum-gravity effects. Our analysis indicates that phase-locked, short-time overlap fits on kilogram-scale optical-spring modes can tighten this bound by orders of magnitude. We outline two implementable measurement pipelines -- continuous back-action-evading single-quadrature readout and stroboscopic, phase-locked pulsed tomography -- that exploit this leverage, making QSL-based timing a practical, near-term probe of minimal-length physics on quantum-optical and optomechanical platforms.

DOI
10.1103/jfbx-l1zw

Related papers

Coherent states in minimal-length Quantum Mechanics: inequivalent characterizations and emergent squeezing

Giuseppe Gaetano Luciano, Pasquale Bosso, Daniel Chemisana

Several approaches to quantum gravity suggest the emergence of a fundamental minimal length at the Planck scale. In quantum mechanics, this feature is naturally encoded through deformations of the Heisenberg algebra, leading to the Generalized Uncertainty Principle (GUP). While the phenomenological implications of GUP have been extensively explored, a consistent characterization of coherent states in minimal-length quantum mechanics remains elusive. In this work, we present a systematic analysis of coherent states for the one-dimensional harmonic oscillator. We show that the canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. We then investigate the dynamical and semiclassical consequences of this inequivalence by comparing the evolution of generalized coherent states with that of states saturating the GUP. In particular, we demonstrate that minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics. These results establish a unified framework for coherence in GUP-based quantum theories and identify distinctive semiclassical signatures of minimal-length physics, opening a new avenue for probing quantum-gravitational effects.

quant-pharXiv:2607.01393•Jul 3, 2026•0 citations

Probing quantum commutators

Matteo A. C. Rossi, Tommaso Giani, Matteo G. A. Paris

Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on the position measurement has a lower bound. The value of the minimal length is not predicted by theories and must be evaluated experimentally. In this paper, we address the quantum bound to estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra of the Hilbert subspace.

•Jun 10, 2016•0 citations

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

Salman Sajad Wani, Aatif Kaisar Khan, Saif Al-Kuwari +1 more

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.

quant-pharXiv:2511.20707•Physics Letters A•Nov 26, 2025•1 citation

Probing deformed quantum commutators

Matteo A. C. Rossi, Tommaso Giani, Matteo G. A. Paris

Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.

arXiv:1606.03420•Physical review. D/Physical review. D.•Jul 6, 2016•19 citations

Probing Planck-scale spacetime by cavity opto-atomic $^{87}$Rb interferometry

Mohsen Khodadi, Kourosh Nozari, Anha Bhat +1 more

The project of quantum spacetime phenomenology focuses on searching pragmatically for the Planck-scale quantum features of spacetime. Among these features is the existence of a characteristic length scale commonly addressed by effective approaches to quantum gravity (QG). This characteristic length scale could be simply realized, for instance, by generalizing the standard Heisenberg uncertainty principle to a generalized uncertainty principle (GUP). While it is usually expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a cold atomic ensemble recoil experiment (CARE) as a low-energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high-finesse optical cavity that is supported by a new class of low-power-consumption integrated devices known as micro-electro-opto-mechanical systems. In the framework of a top-down-inspired bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant from the rubidium (⁠|$^{87}$|Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint of |$0.999\,978 <\lambda_0<1.000\,02$| for the dimensionless characteristic parameter. Our study shows that the best playground to test QG approaches is not merely high-energy physics, but a table-top nanosystem assembly as well. PACS numbers: 04.60.-m, 04.60.Bc

arXiv:1804.06389•Progress of Theoretical and Experimental Physics•Apr 2, 2019•14 citations

Experimental Signature of Gravitational Decoherence from a Minimal Semiclassical Extension A 1 Hz Target for Levitated Optomechanics

Yi Ning Chen

Laboratory-based experimental tests remain a central challenge in the study of the quantum-gravity interface. We present a quantitative, experimentally testable prediction for gravitationally induced quantum decoherence of spatial superpositions in levitated optomechanical systems. Starting from two independently well-tested physical elements—the quantum nature of material energy-momentum fluctuations (established in particle physics) and the linear response kernel of classical geometry (derived from the weak-field limit of general relativity and verified by gravitational-wave observations)—and supplementing them with a minimal extension postulate for superposition states, we obtain a rigid scaling law for the gravitational decoherence rate: \Gamma \sim G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L), where M is the mass of the object, d the spatial separation of the superposition branches, L the characteristic linear dimension, and \Phi a dimensionless function encoding the unknown ultraviolet cutoff scale l_* of the effective geometric noise. The structural form \Gamma \propto M^2 d^2 / L^3 contains no free adjustable parameters; the overall amplitude is set by the choice of l_*. Identifying l_* with the Planck length \ell_P = \sqrt{\hbar G / c^3}—the only known scale bridging quantum theory and gravity—yields \Phi \sim \mathcal{O}(1) and a specific numerical target. For current levitated nanoparticle experiments (M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, L \sim 10^{-6}\,\text{m}), this Planck-scale hypothesis predicts a decoherence rate of order 1\,\text{Hz}, placing it within the foreseeable sensitivity window of next-generation optomechanical setups. We discuss the exclusive physical signatures distinguishing this mechanism from environmental decoherence channels and outline explicit falsification conditions, providing experimental groups with a concrete target to probe the quantum-gravity interface in the laboratory.

•May 20, 2026•0 citations
Many quantum-gravity scenarios predict a minute modification of the canonical commutator, known as the generalized uncertainty principle (GUP), whose low-energy signatures are, in principle, accessible to state-of-the-art laboratory tests. We compute first-order minimal-length corrections to the quantum speed limit (QSL) for three cases: uniform superpositions in an infinite square well, coherent harmonic-oscillator states, and squeezed-oscillator states. We identify a universal amplification law: for any pure state, the fractional shift of either speed limit scales linearly with βββ and algebraically with the state's effective Hilbert-space size. As the effective Hilbert-space dimension can be exceedingly large, the associated minimal-length signatures are amplified by several orders of magnitude. Using high-precision matter-wave timing data, we set a direct bound on the GUP parameter βββ, which quantifies minimal-length quantum-gravity effects. Our analysis indicates that phase-locked, short-time overlap fits on kilogram-scale optical-spring modes can tighten this bound by orders of magnitude. We outline two implementable measurement pipelines -- continuous back-action-evading single-quadrature readout and stroboscopic, phase-locked pulsed tomography -- that exploit this leverage, making QSL-based timing a practical, near-term probe of minimal-length physics on quantum-optical and optomechanical platforms.
Several approaches to quantum gravity suggest the emergence of a fundamental minimal length at the Planck scale. In quantum mechanics, this feature is naturally encoded through deformations of the Heisenberg algebra, leading to the Generalized Uncertainty Principle (GUP). While the phenomenological implications of GUP have been extensively explored, a consistent characterization of coherent states in minimal-length quantum mechanics remains elusive. In this work, we present a systematic analysis of coherent states for the one-dimensional harmonic oscillator. We show that the canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. We then investigate the dynamical and semiclassical consequences of this inequivalence by comparing the evolution of generalized coherent states with that of states saturating the GUP. In particular, we demonstrate that minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics. These results establish a unified framework for coherence in GUP-based quantum theories and identify distinctive semiclassical signatures of minimal-length physics, opening a new avenue for probing quantum-gravitational effects.
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on the position measurement has a lower bound. The value of the minimal length is not predicted by theories and must be evaluated experimentally. In this paper, we address the quantum bound to estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra of the Hilbert subspace.
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 −p4/(8m3c2)-p^{4}/(8 m^{3} c^{2})−p4/(8m3c2) 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 ε2t2ε^{2} t^{2}ε2t2 phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron (ε≈1.5×10−10ε\approx 1.5\times 10^{-10}ε≈1.5×10−10) in a 5.4 T5.4\,\mathrm{T}5.4T Penning trap, read out with 149 GHz149\,\mathrm{GHz}149GHz quantum-limited balanced homodyne, should reveal this drift within ∼15 min\sim 15\,\mathrm{min}∼15min -- 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.
Several quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose their physical meaning. In quantum mechanics, the insurgence of such a minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on position measurements has a lower bound. The value of the minimal length is not predicted by theories and must be estimated experimentally. In this paper, we address the quantum bound to the estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra induced by the deformed commutation relations.
Probing Planck-scale spacetime by cavity opto-atomic 87^{87}87Rb interferometry
The project of quantum spacetime phenomenology focuses on searching pragmatically for the Planck-scale quantum features of spacetime. Among these features is the existence of a characteristic length scale commonly addressed by effective approaches to quantum gravity (QG). This characteristic length scale could be simply realized, for instance, by generalizing the standard Heisenberg uncertainty principle to a generalized uncertainty principle (GUP). While it is usually expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a cold atomic ensemble recoil experiment (CARE) as a low-energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high-finesse optical cavity that is supported by a new class of low-power-consumption integrated devices known as micro-electro-opto-mechanical systems. In the framework of a top-down-inspired bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant from the rubidium (⁠|87^{87}87|Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint of |0.999 978<λ0<1.000 020.999\,978 <\lambda_0<1.000\,020.999978<λ0​<1.00002| for the dimensionless characteristic parameter. Our study shows that the best playground to test QG approaches is not merely high-energy physics, but a table-top nanosystem assembly as well. PACS numbers: 04.60.-m, 04.60.Bc
Laboratory-based experimental tests remain a central challenge in the study of the quantum-gravity interface. We present a quantitative, experimentally testable prediction for gravitationally induced quantum decoherence of spatial superpositions in levitated optomechanical systems. Starting from two independently well-tested physical elements—the quantum nature of material energy-momentum fluctuations (established in particle physics) and the linear response kernel of classical geometry (derived from the weak-field limit of general relativity and verified by gravitational-wave observations)—and supplementing them with a minimal extension postulate for superposition states, we obtain a rigid scaling law for the gravitational decoherence rate: \Gamma \sim G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L), where M is the mass of the object, d the spatial separation of the superposition branches, L the characteristic linear dimension, and \Phi a dimensionless function encoding the unknown ultraviolet cutoff scale l_* of the effective geometric noise. The structural form \Gamma \propto M^2 d^2 / L^3 contains no free adjustable parameters; the overall amplitude is set by the choice of l_*. Identifying l_* with the Planck length \ell_P = \sqrt{\hbar G / c^3}—the only known scale bridging quantum theory and gravity—yields \Phi \sim \mathcal{O}(1) and a specific numerical target. For current levitated nanoparticle experiments (M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, L \sim 10^{-6}\,\text{m}), this Planck-scale hypothesis predicts a decoherence rate of order 1\,\text{Hz}, placing it within the foreseeable sensitivity window of next-generation optomechanical setups. We discuss the exclusive physical signatures distinguishing this mechanism from environmental decoherence channels and outline explicit falsification conditions, providing experimental groups with a concrete target to probe the quantum-gravity interface in the laboratory.