Related papers: Optimal dual quantizers of $1D$ $\log$-concave dis…
In this paper we establish the sharp rate of the optimal dual quantization problem. The notion of dual quantization was recently introduced in the paper [8], where it was shown that, at least in an Euclidean setting, dual quantizers are…
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…
We prove that, for any measurable phase space subset $\Omega\subset\mathbb{R}^{2d}$ with $0<|\Omega|<\infty$ and any $1\le p < \infty$, the nonlinear concentration problem $$ \sup_{f \in…
In this paper, we first consider a flat plate (called a lamina) with uniform density $\rho$ that occupies a region $\mathfrak R$ of the plane. We show that the location of the center of mass, also known as the centroid, of the region equals…
In this paper, we study the approximation and estimation of $s$-concave densities via R\'enyi divergence. We first show that the approximation of a probability measure $Q$ by an $s$-concave densities exists and is unique via the procedure…
We consider a channel with a binary input X being corrupted by a continuous-valued noise that results in a continuous-valued output Y. An optimal binary quantizer is used to quantize the continuous-valued output Y to the final binary output…
We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity. The nonlocal nature of the operator and the absence of…
In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the…
Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum…
Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This…
This paper studies estimation of and inference on a distribution function $F$ that is concave on the nonnegative half line and admits a density function $f$ with potentially unbounded support. When $F$ is strictly concave, we show that the…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
In this paper, we propose two linearized finite difference schemes for solving the logarithmic Schr\"odinger equation (LogSE) without the need for regularization of the logarithmic term. These two schemes employ the first-order and the…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
We introduce the Clifford entropy, a measure of how close an arbitrary unitary is to a Clifford unitary, which generalizes the stabilizer entropy for states. We show that this quantity vanishes if and only if a unitary is Clifford, is…
Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this…
In this paper, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of…