We study the fundamental properties of the quantum f -relative entropy, where f(·) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they hold for a class of operator convex functions, and different for f(t) = − ln(t) from, the previously known conditions. The quantum f -entropy is defined in...

We investigate compactness properties of the Riemann–Liouville operator Rα of fractional integration when regarded as operator from L2[0, 1] into C(K), the space of continuous functions over a compact subset K in [0, 1]. Of special interest are small sets K, i.e. those possessing Lebesgue measure zero (e.g. fractal sets). We prove upper estimates for the Kolmogorov numbers of Rα against certain...

We study the ground state of a gapped quantum many-body system whose entanglement entropy SA can be expressed as SA = a|∂A| − γ , where a,γ are some constants and |∂A| is an area of the subsystem A. By using a recently proved operator extension of strong subadditivity of entropy [I. H. Kim, J. Math. Phys. 53, 122204 (2012)], we show that a certain linear combination of the real-space entangleme...

Recently, different semantics for relational probabilistic conditionals and corresponding maximum entropy (ME) inference operators have been proposed. In this paper, we study the so-called aggregation semantics that covers both notions of a statistical and subjective view. The computation of its inference operator requires the calculation of the ME-distribution satisfying all probabilistic cond...

This paper presents new methods for probabilistic belief revision and information fusion. By making use of the principles of optimum entropy (ME-principles), we define a generalized revision operator which aims at simulating the human learning of lessons, and we introduce a fusion operator which handles probabilistic information faithfully. In general, this fusion operator computes kind of mean...

An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator indicates how the quantum geometry of non-rotating isolated horizons can be generalized to rotating ones and how the recent computations of black hole entrop...

This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are ob...

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational princi...

Similar to fuzzy set on a possibility space, uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Entropy provides a quantitative measurement of the uncertainty associated with an uncertain set. This paper presents a formula for calculating the entropy of an uncertain set via its inverse membership function. Based on the formula, the entropy op...

Given a unitary operator, in the context of quantum information 1 , one may ask how much entanglement capability the operator has. The entangling unitary operator can be considered as a resource for quantum-information processing, and it becomes important to quantitatively describe unitary operators. Recently, there is increasing interest in the entanglement capabilities of quantum evolution an...