Related papers: Converse Bounds for Entropy-Constrained Quantizati…
We consider the joint source-channel coding problem of sending a Gaussian source on a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of…
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic…
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…
We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables $(X_1, X_2, \dots, X_n)$ possessing a symmetric joint distribution. Our lower bound is in terms of the joint entropy of $(X_1, X_2, \dots,…
We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
We consider the optimal quantization problem with R\'enyi-$\alpha$-entropy constraints for centered Gaussian measures on a separable Banach space. For $\alpha = \infty$ we can compute the optimal quantization error by a moment on a ball.…
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…
This paper studies the fundamental limits of the minimum average length of lossless and lossy variable-length compression, allowing a nonzero error probability $\epsilon$, for lossless compression. We give non-asymptotic bounds on the…
In this paper, we revisit two multi-terminal lossy source coding problems: the lossy source coding problem with side information available at the encoder and one of the two decoders, which we term as the Kaspi problem (Kaspi, 1994), and the…
Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces,…
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…
We define the entropic bounds, i.e minimal uncertainty for pairs of unitary testers in distinguishing between unitary transformations not unlike the well known entropic bounds for observables. We show that in the case of specific sets of…
We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verd\'{u} for general probability measures. A second bound improves the tightness of an inequality by…
Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…