Related papers: A strengthened data processing inequality for the …
We prove regularity estimates for functions which are harmonic with respect to certain jump processes. The aim of this article is to extend the method of Bass-Levin[BL02] and Bogdan-Sztonyk[BS05] to more general processes. Furthermore, we…
The exponential ergodicity of partially dissipative McKean-Vlasov SDEs in the \(L^1\)-Wasserstein distance has been extensively studied using asymptotic reflection coupling. However, the reflection coupling method is not applicable for the…
Fawzi and Fawzi recently defined the sharp R\'enyi divergence, $D_\alpha^\#$, for $\alpha \in (1, \infty)$, as an additional quantum R\'enyi divergence with nice mathematical properties and applications in quantum channel discrimination and…
This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…
Existing error-bound-based analyses for stochastic algorithms that exhibit certain descent properties, such as randomized coordinate descent and randomized projection methods, are often limited in scope and typically lead to overly…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variable observables. This inequality is more sensitive than the previously established EPR inequality based on inferred variances, and…
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
We consider a two-parameter family of R\'enyi relative entropies $D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative entropies (or…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for…
We prove additivity violation of minimum output entropy of quantum channels by straightforward application of \epsilon-net argument and L\'evy's lemma. The additivity conjecture was disproved initially by Hastings. Later, a proof via…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential…
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…
Thermodynamic extensivity is commonly introduced as a postulate -- the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property from microscopic conditions on the pair potential, without…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
We prove an almost optimal hypercontractive inequality for products of quantum erasure channels, generalizing the hypercontractivity for classical binary erasure channels. To our knowledge, this is the first tensorization-type…