Related papers: Convex Split Lemma without Inequalities
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $\ln d_a$ to the von Neumann entropy, where $d_a$ is the…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Recent advances in large language models (LLMs) have revolutionized natural language processing, yet evaluating their intrinsic linguistic understanding remains challenging. Moving beyond specialized evaluation tasks, we propose an…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is…
The Maximum Mutual Information (MMI) criterion is different from the Least Error Rate (LER) criterion. It can reduce failing to report small probability events. This paper introduces the Channels Matching (CM) algorithm for the MMI…
Higher-order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication that are invisible to…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation…
We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
The first two authors of this paper asserted in Lemma 4 of "New Farkas-type constraint qualifications in convex infinite programming" (DOI: 10.1051/cocv:2007027) that a given reverse convex inequality is consequence of a given convex system…
We discuss linear programming techniques that help to deduce corollaries of non classic inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown)…
We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present…