Related papers: Tight relations and equivalences between smooth re…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading order corrections to asymptotic i.i.d.~limits. Here, we comprehensively study the use of it to…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
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…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
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…
Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy…
The measured relative entropy and measured R\'enyi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or R\'enyi relative entropy…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…