Related papers: Log-majorization and matrix norm inequalities with…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This…
We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm controls of Calder\'on-Zygmund operators and their associated commutators in the above mention spaces.
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies…
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated.…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
Recently, the spectral geometric mean has been studied by some papers. In this paper, we firstly estimate the H\"{o}lder type inequality of the spectral geometric mean of positive invertible operators on the Hilbert space for all real order…
We establish two inequalities in real inner product spaces. The first is a multiplicative strengthening of the classical Hornich-Hlawka inequality: for all vectors $x, y, z$ in a real inner product space $H$ \[ \|x\|\,\|y\| +…
Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the…
This paper undertakes a thorough investigation of matrix means interpolation and comparison. We expand the parameter $\vartheta$ beyond the closed interval $[0,1]$ to cover the entire positive real line, denoted as $\mathbb{R}^+$.…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
The optimal transport map between the standard Gaussian measure and an $\alpha$-strongly log-concave probability measure is $\alpha^{-1/2}$-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic…
Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. We show that a…
In [4] Camps-Moreno et al. treated (relative) generalized Hamming weights of codes from extended norm-trace curves and they gave examples of resulting good asymmetric quantum error-correcting codes employing information on the relative…