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Security proofs in quantum cryptography rely on conditional entropies. In a many-round protocol, their estimation is a challenging task; one must account for the most general attacks by an eavesdropper, including those that are not…

Quantum Physics · Physics 2026-05-29 Lewis Wooltorton , Peter Brown , Omar Fawzi

It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular…

Quantum Physics · Physics 2007-05-23 Michael J. W. Hall

Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…

Quantum Physics · Physics 2020-07-20 Anurag Anshu , Mario Berta , Rahul Jain , Marco Tomamichel

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…

Quantum Physics · Physics 2021-11-23 Tom Gur , Min-Hsiu Hsieh , Sathyawageeswar Subramanian

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…

Classical Physics · Physics 2016-10-03 Rudolf Hanel , Stefan Thurner , Murray Gell-Mann

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…

Quantum Physics · Physics 2022-10-05 Frederic Dupuis , Omar Fawzi , Renato Renner

The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…

Quantum Physics · Physics 2019-06-05 P. Boes , J. Eisert , R. Gallego , M. P. Mueller , H. Wilming

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

Metric Geometry · Mathematics 2020-12-17 Tom Leinster , Emily Roff

Entanglement is considered a fundamental ingredient for quantum technologies and condensed matter systems are among the good candidates for quantum devices. For bipartite pure states the von Neumann entropy is a proper measure of…

Quantum Physics · Physics 2023-03-15 T. Pauletti , M. Garcia , G. A. Canella , V. V. França

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…

Statistical Mechanics · Physics 2009-11-11 Israel Klich , Gil Refael , Alessandro Silva

Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…

Quantum Physics · Physics 2007-05-23 Nikolaos P. Papadakos

We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

Quantum Physics · Physics 2024-11-20 Simon Becker , Nilanjana Datta , Michael G. Jabbour

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…

Information Theory · Computer Science 2007-07-13 Chengshi Liu

In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…

Information Theory · Computer Science 2020-08-13 Mladen Kovačević , Ivan Stanojević , Vojin Šenk

This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…

Physics and Society · Physics 2025-03-27 Yujie Shi , Alex Jie Yang , Sanhong Deng

The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and…

Quantum Physics · Physics 2019-01-30 Giorgia Minello , Luca Rossi , Andrea Torsello

Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…

Information Theory · Computer Science 2023-08-23 Holger Metzler , Carlos A. Sierra

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

Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…

Statistical Mechanics · Physics 2015-03-19 Stefan Thurner , Rudolf Hanel

We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to…