Related papers: Axiomatic approach to contextuality and nonlocalit…
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality)…
In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched R\'enyi divergences such as the sandwiched R\'enyi conditional entropy. We follow three different approaches: The first one is the "almost…
Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, and computation. We introduce a graph-based approach to derive classicality inequalities that bound local,…
In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…
We study the power of dephasing-covariant operations in the resource theories of coherence and entanglement. These are quantum operations whose actions commute with a projective measurement. In the resource theory of coherence, we find that…
We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a…
We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced…
Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are…
Transformer architectures have achieved remarkable empirical success in modeling contextual relations, yet a clear understanding of their expressive power is still lacking. In this work, we introduce a measure-theoretic framework in which…
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches…
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to…
A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure $\nu$ on the Cantor space $\C$ and any suitable complexity class $C \subseteq \C$, the theory identifies the subsets…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
Although it is well known that the amount of resources that can be asymptotically distilled from a quantum state or channel does not exceed the resource cost needed to produce it, the corresponding relation in the non-asymptotic regime…
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics…
Quantum resource theories allow us to quantify a useful quantum phenomenon, to develop new protocols for its detection and determine the exact processes that maximize its use for practical tasks. These theories aim at transforming physical…
We define am axiomatic timeless framework for asynchronous distributed systems, together with well-formedness and consistency axioms, which unifies and generalizes the expressive power of current approaches. 1) It combines classic…
There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the…