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In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. This class of channels was introduced in , where its product… (More)
We discuss a family of estimators for the entropy rate of a stationary ergodic process and prove their pointwise and mean consistency under a Doeblin-type mixing condition. The estimators are Cesàro averages of longest match-lengths, and their consistency follows from a generalized ergodic theorem due to Maker. We provide examples of their performance on… (More)
A number of simple inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. 1 The weighted Gibbs inequality and its consequences The definition and initial results on weighted entropy were introduced in [1, 14]. Further progress was made, subsequently, in [27, 9, 17, 26, 28, 34, 18],… (More)
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. 2000 MSC. 60A10, 60B05, 60C05
We analyse an analog of the entropy-power inequality for the weighted entropy. In particular, we discuss connections with weighted Lieb‘s splitting inequality and an Gaussian additive noise formula. Examples and counterexamples are given, for some classes of probability distributions.
The aim of this paper is to analyze the weighted KyFan inequality proposed in . A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an improvement of the standard KyFan inequality.