相关论文: Quantization dimensions of compactly supported pro…
The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…
Majorization is a stochastic ordering relation that compares the relative diversity of probability distributions with numerous applications in econometrics, spectral theory, and ecology. It is well-known that the majorization partial order…
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.…
The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible…
The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue \textit{per se} and because these measures, which are functionals of the single-particle probability density of the systems, describe…
Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every $d\geq 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
We give a short proof that there exists a countable state Bernoulli measure maximizing the dimension of their images under the continued fraction expansion.
This paper investigates the relationship between quantization of measures and metric mean dimension of topological dynamical systems. We introduce the concept of mean quantization dimension for invariant probability measures and establish a…
Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on $\br^d$, as extensions of the notions of Bessel and frame spectra that correspond to bases of…
Let $P:=\frac 1 3 P\circ S_1^{-1}+\frac 13 P\circ S_2^{-1}+\frac 13\nu$, where $S_1(x)=\frac 15 x$, $S_2(x)=\frac 1 5 x+\frac 45$ for all $x\in \mathbb R$, and $\nu$ be a Borel probability measure on $\mathbb R$ with compact support. Such a…
The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric…
In this paper we study multipartite and correlated majorization of the finite discrete probability distributions emerging in quantum information theory. We start proving the subadditivity of the R\'{e}nyi and Burg entropies, and we show…
The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…
We study systematically resource measures of coherence and entanglement based on R\'enyi relative entropies, which include the logarithmic robustness of coherence, geometric coherence, and conventional relative entropy of coherence together…
Let $R$ be a finite dimensional $k$-algebra over an algebraically closed field $k$ and $\mathrm{mod} R$ be the category of all finitely generated left $R$-modules. For a given full subcategory $\mathcal{X}$ of $\mathrm{mod} R,$ we denote by…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum,…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…