Related papers: Relations between different quantum R\'enyi diverg…
The concept of the smoothing parameter plays a crucial role in both lattice-based and code-based cryptography, primarily due to its effectiveness in achieving nearly uniform distributions through the addition of noise. Recent research by…
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum…
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
Recently, a new notion of quantum R\'enyi divergences has been introduced by M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.Math.Phys. 54:122203, (2013), and Wilde, Winter, Yang, Commun.Math.Phys. 331:593--622, (2014), that has…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
We study an extension of the sandwiched R\'enyi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $\alpha\in [1/2,1)$. This work is intended as a continuation of [A. Jen\v{c}ov\'a, Ann. Henri…
For $\alpha,z>0$ with $\alpha\ne1$, motivated by comparison between different kinds of R\'enyi divergences in quantum information, we consider log-majorization between the matrix functions \begin{align*}…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
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 describe a quantum algorithm to estimate the $\alpha$-Renyi entropy of an unknown density matrix $\rho\in\mathcal{C}^{d\times d}$ for $\alpha\neq 1$ by combining the recent technique of quantum singular value transformations with the…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…
Recent studies have introduced the worst-case quantum divergence as a key measure in quantum information. Here we show that such divergences can be understood from the perspective of the resource theory of asymmetric distinguishability,…
A noteworthy discovery is that the minimal evolution time is smaller for parity-time ($\mathcal{PT}$) symmetric systems compared to Hermitian setups. Moreover, there is a significant acceleration of two-qubit quantum entanglement…
In this paper, we study the approximation and estimation of $s$-concave densities via R\'enyi divergence. We first show that the approximation of a probability measure $Q$ by an $s$-concave densities exists and is unique via the procedure…
Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two…
We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator $\sum_i (-\Delta_i)^s$ and the interaction potential of the form $\sum_i \delta_i^{-2s}$ where $\delta_i$ is the nearest-neighbor…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…