Related papers: Properties of the Strong Data Processing Constant …
The noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions. For instance, the worst-case ratio of output relative entropy to input relative entropy for all possible pairs of input…
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…
The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. Various…
It is well-known that any quantum channel $\mathcal{E}$ satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum $\chi^2_{\kappa}$divergences and quantum relative entropy. More specifically, the…
Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality…
Data-processing is a desired property of classical and quantum divergences and information measures. In information theory, the contraction coefficient measures how much the distinguishability of quantum states decreases when they are…
The sandwiched R\'enyi divergences of two finite-dimensional density operators quantify their asymptotic distinguishability in the strong converse domain. This establishes the sandwiched R\'enyi divergences as the operationally relevant…
There are different inequivalent ways to define the R\'enyi capacity of a channel for a fixed input distribution $P$. In a 1995 paper Csisz\'ar has shown that for classical discrete memoryless channels there is a distinguished such quantity…
Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained.…
Let $\nu$ and $\mu$ be probability distributions on $\mathbb{R}^n$, and $\nu_s,\mu_s$ be their evolution under the heat flow, that is, the probability distributions resulting from convolving their density with the density of an isotropic…
We extend the Rate-Distortion-Perception (RDP) framework to the R\'enyi information-theoretic regime, utilizing Sibson's $\alpha$-mutual information to characterize the fundamental limits under distortion and perception constraints. For…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately…
In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of…
Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential…
In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding…
One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured…
This paper establishes the exact strong converse exponent of the soft covering problem in the classical setting. This exponent characterizes the slowest achievable convergence speed of the total variation to one when a code of rate below…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
Given two density matrices $\rho$ and $\sigma$, there are a number of different expressions that reduce to the $\alpha$-R\'enyi relative entropy of $\rho$ with respect to $\sigma$ in the classical case; i.e., when $\rho$ and $\sigma$…