Related papers: Convexity of quantum $\chi^2$-divergence
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…
This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
In this paper we consider the $\chi$-function (the Holevo capacity of constrained channel) and the convex closure of the output entropy for arbitrary infinite dimensional channel. It is shown that the $\chi$-function of an arbitrary channel…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
The generalized Marcum functions $Q_{\mu}(x,y)$ and $P_{\mu}(x,y)$ have as particular cases the non-central $\chi^2$ and gamma cumulative distributions, which become central distributions (incomplete gamma function ratios) when the…
This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
The maximal correlation coefficient measures the linear correlation in a bipartite distribution and contraction coefficients measure how much information is lost under a noisy channel. Remarkably, Raginsky established a close relation…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
Fawzi and Fawzi recently defined the sharp R\'enyi divergence, $D_\alpha^\#$, for $\alpha \in (1, \infty)$, as an additional quantum R\'enyi divergence with nice mathematical properties and applications in quantum channel discrimination and…
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We present a quantum algorithm to compute the discrete Legendre-Fenchel transform. Given access to a convex function evaluated at $N$ points, the algorithm outputs a quantum-mechanical representation of its corresponding discrete…