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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…

Quantum Physics · Physics 2026-02-02 Gereon Koßmann , René Schwonnek

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…

Quantum Physics · Physics 2021-09-01 Sathyawageeswar Subramanian , Min-Hsiu Hsieh

The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…

Mathematical Physics · Physics 2016-09-26 Hadi Reisizadeh , S. Mahmoud Manjegani

We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple…

Information Theory · Computer Science 2022-03-29 Michael G. Jabbour , Nilanjana Datta

Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for…

Quantum Physics · Physics 2014-12-23 Nelly Huei Ying Ng , Mario Berta , Stephanie Wehner

It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…

Quantum Physics · Physics 2015-05-20 M. E. Shirokov

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

Information Theory · Computer Science 2022-05-30 Kenneth Bogert

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…

Machine Learning · Computer Science 2019-10-31 Lukas Gonon , Lyudmila Grigoryeva , Juan-Pablo Ortega

We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…

Quantum Physics · Physics 2015-06-18 S. Zozor , G. M. Bosyk , M. Portesi

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

Quantum Physics · Physics 2015-03-20 Marco Tomamichel

Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi…

Strongly Correlated Electrons · Physics 2022-06-15 Yi-Ting Tu , Yu-Chin Tzeng , Po-Yao Chang

Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…

Quantum Physics · Physics 2017-05-22 Alexey E. Rastegin

Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…

Information Theory · Computer Science 2026-02-02 Roberto Rubboli , Erkka Haapasalo , Marco Tomamichel

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…

Quantum Physics · Physics 2026-05-27 Sreejith Sreekumar , Ziv Goldfeld , Mark M. Wilde

Quantum physical layer security protocols offer significant advantages, particularly in space communications, but their achievable secrecy rates are often limited to the asymptotic regime. Realistic communication systems, however, demand…

Quantum Physics · Physics 2025-02-10 Masahito Hayashi , Angeles Vázquez-Castro

This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…

Quantum Physics · Physics 2018-12-14 Christoph Hirche

This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs…

Quantum Physics · Physics 2025-08-22 Gereon Koßmann , René Schwonnek

R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…

Information Theory · Computer Science 2012-04-13 Marek Śmieja , Jacek Tabor

We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett et al(1995)'s bound based on the R\'enyi entropy of order 2 because the bound…

Information Theory · Computer Science 2016-11-17 Masahito Hayashi

Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…

Risk Management · Quantitative Finance 2024-09-09 Jose Blanchet , Henry Lam , Yang Liu , Ruodu Wang