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Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
Binke Xia, Jingzheng Huang, Yuxiang Yang, Guihua Zeng
https://arxiv.org/abs/2510.09216 https://

Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of quantum gates or probes. However, this conventional perspective fails to interpret recent studies of "super-Heisenberg" scaling, where precision improves faster than linearly with T and N. In this work, we revisit the Heisenberg scaling by leveraging the position-m…

Unique continuation and Hardy's uncertainty principle for hyperbolic Schr\"odinger equations
Torunn Jensen
https://arxiv.org/abs/2510.09202 https://

Unique continuation and Hardy's uncertainty principle for hyperbolic Schrödinger equations
We prove unique continuation properties related to the Hardy uncertainty principle for solutions of the hyperbolic nonlinear Schrödinger equation and the hyperbolic Schrödinger equation with potential. Under suitable conditions on the nonlinearity, or the potential, we show that if $u$ is a solution with Gaussian decay at two different times, then $u\equiv 0$. These results extend to the hyperbolic setting the work of Escauriaza, Kenig, Ponce, and Vega (JEMS, 10, 2008) for the classical SchrÃ…

LIV-Decoherence on Gravitational Cat States
Iarley P. Lobo, Kelvin Sampaio, Gislaine Var\~ao, Moises Rojas, Valdir B. Bezerra
https://arxiv.org/abs/2510.08828 https://

LIV-Decoherence on Gravitational Cat States
Inspired by approaches based on the stochastic generalized uncertainty principle, we propose a Lindblad equation derived from the quantization of a stochastic modified dispersion relation in a Lorentz Invariance Violation (LIV) scenario. This framework enables us to investigate decoherence effects in a system of particles exhibiting gravitationally induced entanglement. We analyze the impact of LIV on entanglement (quantified by concurrence) considering systematic and stochastic effects.

The vOICe vision BCI can in principle also get around the frequency-time uncertainty principle (Heisenberg uncertainty principle) in sound waves, here by exploiting a priori knowledge of the limited set of frequencies used https://www.seeingwithsound.com/freqtime.htm

Risk-Adjusted Policy Learning and the Social Cost of Uncertainty: Theory and Evidence from CAP evaluation
Giovanni Cerulli, Francesco Caracciolo
https://arxiv.org/abs/2510.05007

Risk-Adjusted Policy Learning and the Social Cost of Uncertainty: Theory and Evidence from CAP evaluation
This paper develops a risk-adjusted alternative to standard optimal policy learning (OPL) for observational data by importing Roy's (1952) safety-first principle into the treatment assignment problem. We formalize a welfare functional that maximizes the probability that outcomes exceed a socially required threshold and show that the associated pointwise optimal rule ranks treatments by the ratio of conditional means to conditional standard deviations. We implement the framework using microdata …

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Covering the hypercube, the uncertainty principle, and an interpolation formula
Paata Ivanisvili, Ohad Klein, Roman Vershynin

Replaced article(s) found for cond-mat.stat-mech. https://arxiv.org/list/cond-mat.stat-mech/new
[1/1]:
- Derivation of Bose-Einstein statistics from the uncertainty principle
Paul Tangney

On Sharp Heisenberg Uncertainty Principle and the stability
Xia Huang, Dong Ye
https://arxiv.org/abs/2510.00453 https://arxiv.org/pdf/2510.00453

On Sharp Heisenberg Uncertainty Principle and the stability
In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical harmonic decomposition and the Hardy inequalities, we revise two families of inequalities. We give firstly an affirmative answer in dimension four to Cazacu-Flynn-Lam's conjecture [JFA, 2022] for the sharp Hydrogen Uncertainty Principle, and improve the recent estim…

Quantum speed limit as a sensitive probe of Planck-scale effects
Salman Sajad Wani, Saif Al-Kuwari
https://arxiv.org/abs/2510.00057 https://arxiv.org/pdf/2…

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

A High-Frequency Uncertainty Principle for the Fourier-Bessel Transform
Benjamin Jaye, Rahul Sethi
https://arxiv.org/abs/2509.25500 https://arxiv.org/pdf/2…

A High-Frequency Uncertainty Principle for the Fourier-Bessel Transform
Motivated by problems in control theory concerning decay rates for the damped wave equation $$w_{tt}(x,t) + γ(x) w_t(x,t) + (-Δ+ 1)^{s/2} w(x,t) = 0,$$ we consider an analogue of the classical Paneah-Logvinenko-Sereda theorem for the Fourier Bessel transform. In particular, if $E \subset \mathbb{R}^+$ is $μ_α$-relatively dense (where $dμ_α(x) \approx x^{2α+1}\, dx$) for $α> -1/2$, and $\operatorname{supp} \mathcal{F}_α(f) \subset [R,R+1]$, then we show $$\|f\|_{L^2_α(\mathbb…

Predictively Oriented Posteriors
Yann McLatchie, Badr-Eddine Cherief-Abdellatif, David T. Frazier, Jeremias Knoblauch
https://arxiv.org/abs/2510.01915 https://

Predictively Oriented Posteriors
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a consequence of predictive ability. Doing so leads to inferences which predictively dominate both classical and generalised Bayes posterior predictive distributions: up to logarithmic factors, PrO posteriors converge to the predictively optimal model average at rate $n^…

Symmetrized operators or modified integration measure in Generalized Uncertainty Principle Models
Michael Bishop, Daniel Hooker, Doug Singleton
https://arxiv.org/abs/2509.20466 …

Symmetrized operators or modified integration measure in Generalized Uncertainty Principle Models
Many Generalized Uncertainty Principle (GUP) models modify the inner-product measure to ensure symmetric position or momentum operators. We show that an alternate approach to these GUPs is to symmetrize the operators rather than modifying the inner product. This preserves the standard momentum space allowing the eigenstates and maximally localized states of the modified position operator to have a standard position representation. We compare both approaches and highlight their merits.

The role of angular slit number and angular slit width on the OAM spectrum
Jayson P. Cabanilla, Nathaniel Hermosa
https://arxiv.org/abs/2509.13829 https://…

The role of angular slit number and angular slit width on the OAM spectrum
The uncertainty principle sets the limit for simultaneous measurements of position and momentum, and its angular analogue is realized through angular diffraction. When a beam is spatially confined by angular slits, the uncertainty in its orbital angular momentum (OAM) increases, leading to the generation of OAM sidebands. Both the angular slit number and the angular slit width shapes the spatial confinement of the beam. In this study, we investigate this dependence of the OAM sidebands by obstr…

Far-from-equilibrium thermodynamics of non-Abelian thermal states
Franklin L. S. Rodrigues, Eric Lutz
https://arxiv.org/abs/2510.04788 https://arxiv.org/pd…

Far-from-equilibrium thermodynamics of non-Abelian thermal states
Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems with noncommuting, that is, non-Abelian, conserved quantities. We here derive nonequilibrium generalizations of the second law of thermodynamics in the form of fluctuation relations, both for mechanically and thermally driven quantum systems. We identify a non-A…

Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects
Gaurav Bhandari, S. D. Pathak, Harjit Ghotra
https://arxiv.org/abs/2509.14663 https://

Unified Framework for Geodesic Dynamics with Conservative, Dissipative, and GUP Effects
We derive generalized geodesic equations in curved spacetime that include conservative forces, dissipative effects, and quantum-gravity-motivated minimal-length corrections. Conservative interactions are incorporated through external vector potentials, while dissipative dynamics arise from an exponential rescaling of the particle Lagrangian. Quantum-gravity effects are introduced via Generalized Uncertainty Principle (GUP) deformed Poisson brackets in the Hamiltonian framework. We show that fre…

Localised solution of stochastic Schr\"odinger equation describing simultaneous continuous measurement of position and momentum
Daniel J. Bedingham
https://arxiv.org/abs/2509.11832

Localised solution of stochastic Schrödinger equation describing simultaneous continuous measurement of position and momentum
A stochastic Schrödinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum contingent on the uncertainty principle. The state is understood as that to which the particle tends after a period of continuous measurement. The solution takes the form of a wave packet of fixed Gaussian shape whose centre undergoes random motion in phase space. It…

Quantum hierarchical Fokker-Planck equations with U(1) gauge fields: Application to the Aharonov-Bohm ring
Hyeonseok Yang, Shoki Koyanagi, Yoshitaka Tanimura
https://arxiv.org/abs/2509.11462

Quantum hierarchical Fokker-Planck equations with U(1) gauge fields: Application to the Aharonov-Bohm ring
We investigate a three-dimensional subsystem under a time-dependent U(1) gauge field coupled to rotationally invariant environments. To capture the dynamic behavior of the subsystem under thermal excitations and dissipations, it is imperative to treat the bath in a non-Markovian and nonperturbative manner. This is because quantum noise is constrained by the uncertainty principle, which dictates the relationship between the noise correlation time and the amplitude of the energy fluctuation. To t…