Related papers: Optimal quantization for some triadic uniform Cant…

Using higher-order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical…

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of…

For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…

Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution…

Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists…

This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…

Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with…

We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…

For an integer $q\ge 2$, a perfect $q$-hash code $C$ is a block code over $[q]:=\{1,\ldots,q\}$ of length $n$ in which every subset $\{\mathbf{c}_1,\mathbf{c}_2,\dots,\mathbf{c}_q\}$ of $q$ elements is separated, i.e., there exists…

The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…

In this paper, we have considered a uniform distribution on a regular polygon with $k$-sides for some $k\geq 3$ and the set of all its $k$ vertices as a conditional set. For the uniform distribution under the conditional set first, for all…

We estimate the distribution of relatively $r$-prime lattice points in number fields $K$ with their components having a norm less than $x$. In the previous paper we obtained uniform upper bounds as $K$ runs through all number fields under…

We establish several optimal estimates for exceptional parameters in the projection of fractal measures: (1) For a parametric family of self-similar measures satisfying a transversality condition, the set of parameters leading to a…

Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure…

We take advantage of recent and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems,…

Given a probability distribution in R^n with general (non-white) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N =…

We consider optimal scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long…

We consider the optimal quantization problem with R\'enyi-$\alpha$-entropy constraints for centered Gaussian measures on a separable Banach space. For $\alpha = \infty$ we can compute the optimal quantization error by a moment on a ball.…

This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…