Related papers: Brascamp-Lieb Inequalities for Non-Commutative Int…
In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by…
We prove a noncommutative $(p,p)$-Poincar\'e inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our…
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…
The goal of this note is to show that some convolution type inequalities from Harmonic Analysis and Information Theory, such as Young's convolution inequality (with sharp constant), Nelson's hypercontractivity of the Hermite semi-group or…
In this paper, we prove some inequalities for the differences and ratios of the beta function.
We improve the Lieb-Thirring type inequalities by Demuth, Hansmann and Katriel (J. Funct. Anal. 2009) for Schr\"odinger operators with complex-valued potentials. Our result involves a positive, integrable function. We show that in the…
It is known that by dualizing the Bochner-Lichnerowicz-Weitzenb\"{o}ck formula, one obtains Poincar\'e-type inequalities on Riemannian manifolds equipped with a density, which satisfy the Bakry-\'Emery Curvature-Dimension condition…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…
In this paper we investigate the relations between (martingale) BMO spaces, paraproducts and commutators in non-homogeneous martingale settings. Some new, and one might add unexpected, results are obtained. Some alternative proof of known…
We establish an inequality of different metrics for algebraic polynomials.
For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…
In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…
Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and…
In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the…
By differentiating a concavity principle arising from the Pr\'ekopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincar\'e inequality and the Brascamp-Lieb variance inequality. The resulting…
Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even…
Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…
Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…
In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.