相关论文: A generalized skew information and uncertainty rel…

As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties. Unlike the conventional…

It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control [T. Sagawa and M. Ueda, Phys. Rev. Lett. {\bf 104}, 090602 (2010)]. The presence of feedback control in physical systems should…

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

We show that the proof of the generalised quantum Stein's lemma [Brand\~ao & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brand\~ao…

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a…

The invariant response was defined from a formulation of the fluctuation-response theorem in the space of probability distributions. An inequality is here conjectured which sets the mutual information as an upper bound to the invariant…

In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl law.

The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $\chi ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative…

A generalized information formula related to logical probability and fuzzy set is deduced from the classical information formula. The new information measure accords with to Popper's criterion for knowledge evolution very much. In…

Jensen's trace inequality is established for every multivariable, convex function and every trace or trace-like functional on a C*-algebra.

General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…

We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a…

We present new generalized Cline's formula and Jacobson's lemma for the g-Drazin inverse in a ring. These extend many known results, e.g., Chen and Abdolyousefi (Generalized Jacobson's Lemma in a Banach algebra, Comm. Algebra, {\bf…

We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result indicates…

We comment on one of the earliest derivations of the so-called wave-particle duality relation. Our aim is to point out a slight technical flaw in the proof, fixing it. Neither the physical content of the duality relation nor its validity is…