Related papers: Quantum Brascamp-Lieb Dualities
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
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…
We prove sharp $\ell^q L^p$ decoupling inequalities for $p,q \in [2,\infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and…
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
We consider regularized Brascamp-Lieb inequalities using the theory of optimal transportation, more precisely an anisotropic version of Caffarelli's contraction theorem. Furthermore, we provide a full picture concerning the issues of…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many…
We establish a stable form of the general Euclidean Brascamp-Lieb inequality in all cases in which the Lebesgue exponents are strictly between 1 and 2, asserting that all near-extremizers are nearly Gaussian.
We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi…
The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of…
Monogamy of entanglement is the fundamental property of quantum systems. By using two new entanglement measures based on dual entropy, the $S^{t}$-entropy entanglement and $T^{t}_q$-entropy entanglement measures, we present the general…
It is known that many classical inequalities linked to convolutions can be obtained by looking at the monotonicity in time of convolutions of powers of solutions to the heat equation, provided that both the exponents and the coefficients of…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…
We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki--Lieb inequality, which characterize hidden quantum…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…