Related papers: Maximal inequalities in quantum probability spaces
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
We establish sharp Adams type inequalities on Sobolev spaces $W^{\alpha, n/\alpha}(X)$ of any fractional order $\alpha< n$ on Riemannian symmetric space $X$ of noncompact type with dimension $n$ and of arbitrary rank. We also establish…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
I show that the application of the quantum-mechanical (QM) which-way weak measurement scheme of Vaidman may lead to logical inconsistencies. To this end, I study weak values of projection operators. Weak values are (normalized) amplitudes,…
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations…
We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities…
Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, as well as metric versions of the…
Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly,…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
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…
In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann…
We study sum uncertainty relations for arbitrary finite $N$ quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial…
We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ of Hardy-Littlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$…
Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions…