Related papers: Optimal universal bounds for waves with varied coh…
We identify a universal structural principle underlying the smoothing of classical divergences: the optimizer of the smoothing problem is a clipped probability vector, independently of the specific divergence. This yields a…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
Stochastic backgrounds of gravitational waves are intrinsic fluctuations of spacetime which lead to an unavoidable decoherence mechanism. This mechanism manifests itself as a degradation of the contrast of quantum interferences. It defines…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference…
Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for…
In this technical communique we study the maximal robust positively invariant set for state-constrained continuous-time nonlinear systems subjected to a bounded disturbance. Extending results from the theory of barriers, we show that this…
We investigate the majorization order for comparing wave coherence and reveal its fundamental consequences in transport measurements, including power distribution, absorption, transmission, and reflection. We prove that all these…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…
Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework…
Coherence is a defining property of quantum theory that accounts for quantum advantage in many quantum information tasks. Although many coherence quantifiers have been introduced in various contexts, the lack of efficient methods to…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…
We frame the problem of selecting an optimal audio encoding scheme as a supervised learning task. Through uniform convergence theory, we guarantee approximately optimal codec selection while controlling for selection bias. We present…