Related papers: On a Correlation Inequality for Cauchy Type Measur…
We prove a set of inequalities that interpolate the Cauchy-Schwarz inequality and the triangle inequality. Every nondecreasing, convex function with a concave derivative induces such an inequality. They hold in any metric space that…
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…
We propose a new scheme to express the uncertainty principle in form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various…
Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing the iterative methods as regularization methods for this…
We present in detail Thomas Royen's proof of the Gaussian correlation inequality which states that $\mu(K\cap L)\geq \mu(K)\mu(L)$ for any centered Gaussian measure $\mu$ on $R^d$ and symmetric convex sets $K,L$ in $R^d$.
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is…
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data,…
One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we…
The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible…
The ability to measure characteristics of source shapes using non-identical particle correlations is discussed. Both strong-interaction induced and Coulomb induced correlations are shown to provide sensitivity to source shapes. By…
We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation…
We address the problem of whether parties who cannot communicate but share nonsignaling quantum correlations between the outcomes of sharp measurements can distinguish, just from the value of a correlation observable, whether their outcomes…
Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…
We state and prove a Cheeger-like inequality for coexact 1-forms on closed orientable Riemannian manifolds.
We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…