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There are no universally accepted definitions of R\'enyi conditional entropy and R\'enyi mutual information, although motivated by different applications, several definitions have been proposed in the literature. In this paper, we consider…
We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies…
We consider the $k$-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…
Multi-source-extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source-extractors were considered by Kasher and Kempe (for the quantum-independent-adversary and the…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Quantum privacy amplification is a central task in quantum cryptography. Given shared randomness, which is initially correlated with a quantum system held by an eavesdropper, the goal is to extract uniform randomness which is decoupled from…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
The extraction of a physical law y=yo(x) from joint experimental data about x and y is treated. The joint, the marginal and the conditional probability density functions (PDF) are expressed by given data over an estimator whose kernel is…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We consider a distributed quantum hypothesis testing problem with communication constraints, in which the two hypotheses correspond to two different states of a bipartite quantum system, multiple identical copies of which are shared between…
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by…
We introduce and study several notions of computability-theoretic reducibility between subsets of $\omega$ that are "robust" in the sense that if only partial information is available about the oracle, then partial information can be…
Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…
In 2019 Anthony Quas, Philippe Thieullen and Mohamed Zarrabi introduced the concept of strong fast invertibility for linear cocycles. It relates the growth of volumes between different initial times and, together with a condition on…