相关论文: A strengthened data processing inequality for the …
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
Fast development in science and technology has driven the need for proper statistical tools to capture special data features such as abrupt changes or sharp contrast. Many inverse problems in data science require spatiotemporal solutions…
By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the…
We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…
This paper intends to give some new estimates for Tsallis relative operator entropy ${{T}_{v}}\left( A|B \right)=\frac{A{{\natural}_{v}}B-A}{v}$. Let $A$ and $B$ be two positive invertible operators with the spectra contained in the…
It is well-known that the conditional mutual information of a quantum state is zero if, and only if, the quantum state is a quantum Markov chain. Replacing the Umegaki relative entropy in the definition of the conditional mutual information…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure operator. On one hand, by linking this operator with other optimality measures, we…
We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels (i.e. generalized data processing inequality), additivity…
Blind source separation (BSS) is a natural framework for studying how latent causes may be recovered from sensory mixtures, but deriving online and biologically plausible algorithms for structured (i.e., constrained to known domains) and…
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. This class of inequalities has been introduced in the recent…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate…
The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…