相关论文: The Iteration Formula of (n,2,d) Full-correlated M…

Evaluation of the Bellman functions is a difficult task. The exact Bellman functions of the dyadic Carleson Embedding Theorem 1.1 and the dyadic maximal operators are obtained in [3] and [4]. Actually, the same Bellman functions also work…

We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d-dimensional measurement outcomes for which this Bell…

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests…

Elegant Bell inequality is well known for its distinctive property, being maximally violated by maximal entanglement, mutually unbiased bases, and symmetric informationally complete positive operator-valued measure elements. Despite its…

A new explicit closed-form formula for the multivariate $(n, k)$th partial Bell polynomial $B_{n,k} (x_1, x_2, ..., x_{n - k + 1})$ is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily…

The Patterson-Sullivan construction is proved almost surely to recover a Bergman function from its values on a random discrete subset sampled with the determinantal point process induced by the Bergman kernel on the unit ball $\mathbb{D}_d$…

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with $N$ observers, each of which performs one out of two possible three-outcome…

In the celebrated paper [J. Phys. A: Math. Gen. 37, 1775 (2004)], D. Collins and N. Gisin presented for the first time a three setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the…

We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We…

Despite their importance, there is an on-going challenge characterizing multipartite quantum correlations. The Svetlichny and Mermin-Klyshko (MK) inequalities present constraints on correlations in multipartite systems, a violation of which…

Violating Bell's inequalities (BIs) allows one to certify the preparation of entangled states from minimal assumptions -- in a device-independent manner. Finding BIs tailored to many-body correlations as prepared in present-day quantum…

In this paper we prove that the inequality introduced by Collins, Gisin, Linden, Massar and Popescu is tight, or in other words, it is a facet of the convex polytope generated by all local-realistic joint probabilities of d outcomes. This…

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 present an analysis of the structure of Bell inequalities, mainly for the case of N qubits with two observables each. We show that these inequalities are related to Hadamard matrices and define Bell polynomials (in one variable) as an…

We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can…

Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making…

The notion of equivalence of maximally entangled bases of bipartite d-dimensional Hilbert spaces is introduced. An explicit method of inequivalent bases construction is presented.

We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…

The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}. The interacting diffusions pave a way to…