Related papers: Robust Optimality of Gaussian Noise Stability

The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as…

Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the…

We consider the energy norm arising from elliptic problems with discontinuous piecewise constant diffusion. We prove that under the quasi-monotonicity property on the diffusion coefficient, the best approximation error with continuous…

For multi-class classification under class-conditional label noise, we prove that the accuracy metric itself can be robust. We concretize this finding's inspiration in two essential aspects: training and validation, with which we address…

The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the existence…

In the present paper we give proof that the information-transmission capacity of the approximate position measurement with the oscillator energy constraint, which underlies noisy Gaussian homodyning in quantum optics, is attained on…

We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…

Keller and Kindler recently established a quantitative version of the famous Benjamini~--Kalai--Schramm Theorem on noise sensitivity of Boolean functions. The result was extended to the continuous Gaussian setting by Keller, Mossel and Sen…

We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, non-degenerated and stationary Gaussian field $(f(x), {x \in \mathbb R^d})$. Under mild conditions, we…

We pose a fundamental question in computational learning theory: can we efficiently test whether a training set satisfies the assumptions of a given noise model? This question has remained unaddressed despite decades of research on learning…

We propose a quantitative direct method of proving the stability result for Gaussian rough differential equations in the sense of Gubinelli \cite{gubinelli}. Under the strongly dissipative assumption of the drift coefficient function, we…

We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

We establish the irreducibility of stochastic real Ginzburg-Landau equation with $\alpha$-stable noises by a maximal inequality and solving a control problem. As applications, we prove that the system converges to its equilibrium measure…

Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne…

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the…

We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…

We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…

We prove that output-feedback linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in the face of worst-case process and measurement noise distributions when these are independent, stationary, and…

We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized…