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Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…

Quantum Physics · Physics 2025-01-08 Salman Beigi , Christoph Hirche , Marco Tomamichel

We study asymmetric binary channel discrimination, for qantum channels acting on separable Hilbert spaces. We establish quantum Stein's lemma for channels for both adaptive and parallel strategies, and show that under finiteness of the…

Quantum Physics · Physics 2023-08-25 Bjarne Bergh , Jan Kochanowski , Robert Salzmann , Nilanjana Datta

We consider a two-parameter family of R\'enyi relative entropies $D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative entropies (or…

Quantum Physics · Physics 2016-02-23 Koenraad M. R. Audenaert , Nilanjana Datta

Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for $f$-divergences. Universal upper and lower bounds have been provided along with several applications,…

Information Theory · Computer Science 2024-05-16 Lifu Jin , Amedeo Roberto Esposito , Michael Gastpar

Audenaert and Datta recently introduced a two-parameter family of relative R\'{e}nyi entropies, known as the $\alpha$-$z$-relative R\'{e}nyi entropies. The definition of the $\alpha$-$z$-relative R\'{e}nyi entropy unifies all previously…

Quantum Physics · Physics 2015-08-05 Mingyan Simon Lin , Marco Tomamichel

We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…

Quantum Physics · Physics 2019-05-06 Xin Wang , Kun Fang , Runyao Duan

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using R\'{e}nyi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is…

Machine Learning · Computer Science 2024-09-19 Weipeng Huang , Junjie Tao , Changbo Deng , Ming Fan , Wenqiang Wan , Qi Xiong , Guangyuan Piao

Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum…

Quantum Physics · Physics 2023-07-26 Christoph Hirche

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

Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be particularly useful: the Petz quantum Renyi…

Quantum Physics · Physics 2017-01-25 Raban Iten , Joseph M. Renes , David Sutter

Recently, an interesting quantity called the quantum Renyi divergence (or "sandwiched" Renyi relative entropy) was defined for pairs of positive semi-definite operators $\rho$ and $\sigma$. It depends on a parameter $\alpha$ and acts as a…

Quantum Physics · Physics 2014-07-28 Nilanjana Datta , Felix Leditzky

The quantum \chi^2-divergence has recently been introduced and applied to quantum channels (quantum Markov processes). In contrast to the classical setting the quantum \chi^2-divergence is not unique but depends on the choice of quantum…

Mathematical Physics · Physics 2012-10-02 Frank Hansen

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a…

Quantum Physics · Physics 2026-03-31 Satvik Singh , Bjarne Bergh

Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex…

Quantum Physics · Physics 2018-09-13 Xuan-Lun Huang , Jun Gao , Zhi-Qiang Jiao , Zeng-Quan Yan , Ling Ji , Xian-Min Jin

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

The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when…

Quantum Physics · Physics 2021-12-15 Kenji Nakahira

The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…

Quantum Physics · Physics 2022-11-30 Christoph Hirche , Cambyse Rouzé , Daniel Stilck França

The doubly minimized Petz Renyi mutual information of order $\alpha$ is defined as the minimum of the Petz divergence of order $\alpha$ of a given bipartite quantum state relative to all product states. The doubly minimized sandwiched Renyi…

Quantum Physics · Physics 2026-04-07 Laura Burri

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…

Information Theory · Computer Science 2016-03-30 Shashank Singh , Barnabás Póczos

A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…

Quantum Physics · Physics 2020-05-20 Leonardo Banchi , Jason Pereira , Seth Lloyd , Stefano Pirandola