Related papers: Sub-Planck structure quantification in non-Gaussia…
We numerically investigate non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two-point and three-point probability distribution function (PDF) of phase and modulus,…
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…
Leveraging the unique quantum properties of non-Gaussian states is crucial for advancing continuous variable quantum technologies. Recent experimental advancements in generating non-Gaussian states, coupled with theoretical findings of…
We present the experimental investigation of the non-Gaussian nature of some mixtures of Fock states by reconstructing their Wigner function and exploiting two recently introduced measures of non-Gaussianity. In particular, we demonstrate…
Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition…
Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of…
Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving…
We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box--Cox transformations and generalisations thereof. This permits an…
Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
Non-Gaussian states are essential resources in quantum information processing. In this work, we investigate methods for quantifying bosonic non-Gaussianity in many-body systems. Building on recent theoretical insights into the…
We consider the mean field Fokker-Planck equation subject to nonlinear no-flux boundary conditions, which necessarily arise when subjecting a system of Brownian particles interacting via a pair potential in a bounded domain. With the…
Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive) Glauber-Sudarshan $P$-representation. We theoretically and…
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space…
We study the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field…
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.…
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…
The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not…