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The one-class classification problem is a well-known research endeavor in pattern recognition. The problem is also known under different names, such as outlier and novelty/anomaly detection. The core of the problem consists in modeling and…

Computer Vision and Pattern Recognition · Computer Science 2015-03-31 Lorenzo Livi , Alireza Sadeghian , Witold Pedrycz

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

Information Theory · Computer Science 2017-01-04 Günther Koliander , Georg Pichler , Erwin Riegler , Franz Hlawatsch

Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart…

Quantum Physics · Physics 2012-08-30 Omar Fawzi

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…

Quantum Physics · Physics 2009-11-10 Otfried Guehne , Maciej Lewenstein

We provide here a novel algebraic characterization of two information measures associated with a vector-valued random variable, its differential entropy and the dimension of the underlying space, purely based on their recursive properties…

Information Theory · Computer Science 2021-07-12 Juan Pablo Vigneaux

Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…

Quantum Physics · Physics 2017-01-02 Alexey E. Rastegin

We derive a collection of separability conditions for bipartite systems of dimensions d X d which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new…

Quantum Physics · Physics 2009-11-10 Vittorio Giovannetti

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of…

Quantum Physics · Physics 2019-04-26 Neetik Mukherjee , Arunesh Roy , Amlan K. Roy

Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising…

Quantum Physics · Physics 2011-08-04 Aram W. Harrow , Debbie W. Leung

Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…

Strongly Correlated Electrons · Physics 2012-05-16 James R. Wootton

We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the…

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…

Quantum Physics · Physics 2013-05-29 Yu Watanabe , Takahiro Sagawa , Masahito Ueda

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…

Chaotic Dynamics · Physics 2008-06-04 Detlef Holstein

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

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…

Quantum Physics · Physics 2015-09-22 Jun Zhang , Yang Zhang , Chang-shui Yu

Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…

Data Analysis, Statistics and Probability · Physics 2019-07-24 C Granero-Belinchón , S. Roux , P. Abry , N. Garnier

This dissertation is founded on the central notion that structural correlations in dense fluids, such as dense gases, liquids, and glasses, are directly related to fundamental interatomic forces. This relationship was identified early in…

Chemical Physics · Physics 2025-11-11 Brennon L. Shanks

Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of…

High Energy Physics - Theory · Physics 2025-06-24 Shanmuka Shivashankara , Hobbes Sprague

We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Ilya Nemenman