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We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…

Statistics Theory · Mathematics 2025-02-25 Shital Saha , Suchandan Kayal , N. Balakrishnan

Uhlmann's theorem is a cornerstone of quantum information theory, stating that for any quantum state $\rho_{AB}$ and any state $\sigma_A$, there exists an extension $\sigma_{AB}$ of $\sigma_A$ such that the fidelity between $\rho_{AB}$ and…

Quantum Physics · Physics 2026-03-03 Kun Fang , Hamza Fawzi , Omar Fawzi

We show that for any $\alpha>0$ the R\'enyi entropy of order $\alpha$ is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or for a two sided exponential distribution. The…

Information Theory · Computer Science 2021-10-05 Maciej Białobrzeski , Piotr Nayar

We point out a contrasting role the entanglement plays in communication and estimation scenarios. In the first case it brings noticeable benefits at the measurement stage (output super-additivity), whereas in the latter it is the…

Quantum Physics · Physics 2017-07-31 Jan Czajkowski , Marcin Jarzyna , Rafal Demkowicz-Dobrzanski

The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places…

Quantum Physics · Physics 2013-09-02 Aram W. Harrow

We introduce an innovative and mathematically rigorous definition for computing common information from multi-view data, drawing inspiration from G\'acs-K\"orner common information in information theory. Leveraging this definition, we…

Machine Learning · Computer Science 2024-06-24 Qi Zhang , Mingfei Lu , Shujian Yu , Jingmin Xin , Badong Chen

We compute the R\'enyi mutual information of two disjoint spheres in free massless scalar theory in even dimensions higher than two. The spherical twist operator in a conformal field theory can be expanded into the sum of local primary…

High Energy Physics - Theory · Physics 2017-08-16 Bin Chen , Jiang Long

We study data processing inequalities that are derived from a certain class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios are nested alternately. While these information…

Information Theory · Computer Science 2011-09-27 Neri Merhav

We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…

Quantum Physics · Physics 2026-04-07 Bartosz Regula , Marco Tomamichel

A missing piece in quantum information theory, with very few exceptions, has been to provide the random coding exponents for quantum information-processing protocols. We remedy the situation by providing these exponents for a variety of…

Quantum Physics · Physics 2015-09-30 Naresh Sharma

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the…

Quantum Physics · Physics 2020-05-28 Dawei Ding , Hrant Gharibyan , Patrick Hayden , Michael Walter

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Information Theory · Computer Science 2026-05-28 Yanxiao Liu , Yijun Fan , Deniz Gündüz

In this paper, we develop a novel privacy mechanism for Riemannian manifold-valued data. Our key contribution lies in uncovering unexpected connections among geometric analysis, heat diffusion models, and differential privacy (DP). We…

Machine Learning · Statistics 2026-04-23 Xiaotian Chang , Yangdi Jiang , Cyrus Mostajeran , Qirui Hu

The proliferation of optical, electron, and scanning probe microscopies gives rise to large volumes of imaging data of objects as diversified as cells, bacteria, pollen, to nanoparticles and atoms and molecules. In most cases, the…

Machine Learning · Computer Science 2021-05-26 Maxim Ziatdinov , Muammer Yusuf Yaman , Yongtao Liu , David Ginger , Sergei V. Kalinin

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…

Quantum Physics · Physics 2016-03-21 Lin Zhang

We propose an extension of the classical R\'enyi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured…

Quantum Physics · Physics 2025-10-10 Tobias Rippchen , Sreejith Sreekumar , Mario Berta

This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…

Quantum Physics · Physics 2025-02-20 Gilad Gour

We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The R\'enyi mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We…

Statistical Mechanics · Physics 2015-04-16 F. C. Alcaraz , M. A. Rajabpour

A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as…

Quantum Physics · Physics 2025-11-06 Theshani Nuradha , Mark M. Wilde

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…

Quantum Physics · Physics 2009-11-10 N. Boulant , S. Furuta , J. Emerson , T. F. Havel , D. G. Cory