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Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…

Quantum Physics · Physics 2024-08-23 Thomas A. Hahn , Ernest Y. -Z. Tan , Peter Brown

We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…

Quantum Physics · Physics 2023-08-15 George Androulakis , Tiju Cherian John

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…

Quantum Physics · Physics 2018-02-07 Keiji Matsumoto

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…

Information Theory · Computer Science 2010-05-28 Tim van Erven , Peter Harremoës

In this article, we obtain the precise range of the values of the parameter $\alpha$ such that Petz-R\'enyi $\alpha$-relative entropy $D_{\alpha}(\rho||\sigma)$ of two displaced thermal states is finite. More precisely, we prove that, given…

Quantum Physics · Physics 2024-04-18 George Androulakis , Tiju Cherian John

Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences…

Quantum Physics · Physics 2020-08-12 Diego Paiva Pires , Augusto Smerzi , Tommaso Macrì

We derive a new bound on the effectiveness of the Petz map as a universal recovery channel in approximate quantum error correction using the second sandwiched R\'{e}nyi relative entropy $\tilde{D}_{2}$. For large Hilbert spaces, our bound…

Quantum Physics · Physics 2022-03-22 Sam Cree , Jonathan Sorce

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…

Quantum Physics · Physics 2024-05-29 Ke Li , Yongsheng Yao

The sandwiched R\'enyi $\alpha$-divergences of two finite-dimensional quantum states play a distinguished role among the many quantum versions of R\'enyi divergences as the tight quantifiers of the trade-off between the two error…

Quantum Physics · Physics 2025-08-12 Fumio Hiai , Milán Mosonyi

The doubly minimized Petz Renyi mutual information (PRMI) of order $\alpha$ is defined as the minimization of the Petz divergence of order $\alpha$ of a fixed bipartite quantum state $\rho_{AB}$ relative to any product state…

Quantum Physics · Physics 2025-07-08 Laura Burri

In this paper, we discuss the quantum data processing inequality and its refinements that are physically meaningful in the context of approximate recoverability. An important conjecture regarding this due to Seshadreesan et. al. in J. Phys.…

Quantum Physics · Physics 2025-04-17 Saptak Bhattacharya

We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…

High Energy Physics - Theory · Physics 2024-08-27 Jonah Kudler-Flam , Laimei Nie , Akash Vijay

We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…

Machine Learning · Statistics 2023-02-16 Jeremiah Birrell , Yannis Pantazis , Paul Dupuis , Markos A. Katsoulakis , Luc Rey-Bellet

We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces…

Quantum Physics · Physics 2020-06-02 Anna Jencova

Sandwiched (quantum) $\alpha$-R\'enyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications…

Quantum Physics · Physics 2013-12-16 Salman Beigi

Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…

Quantum Physics · Physics 2025-10-02 Yuchen Lu , Kun Fang

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…

Quantum Physics · Physics 2025-09-26 Álvaro Yángüez , Thomas A. Hahn , Jan Kochanowski

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

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy…

Quantum Physics · Physics 2026-02-20 Mario Berta , Hao-Chung Cheng , Yongsheng Yao

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…

Quantum Physics · Physics 2017-11-09 Mario Berta , Omar Fawzi , Marco Tomamichel