Related papers: Computational tools for solving a marginal problem…
Bell inequalities are an important tool for studying non-locality, however quickly become computationally intractable as the system size grows. We consider a novel method for finding an upper bound for the quantum violation of such…
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind…
We establish a relation between the two-party Bell inequalities for two-valued measurements and a high-dimensional convex polytope called the cut polytope in polyhedral combinatorics. Using this relation, we propose a method, triangular…
EPR showed that two particles emitted from a source can be entangled by a shared wavefunction where two non-commuting observables (position, momentum) can be simultaneously real, leading to a contradiction with quantum mechanics (two…
We analyze quantum measurement and entanglement by solving the dynamics of stochastic amplitudes that propagate both forward and backward in time. The model allows simulation of Einstein-Podolsky-Rosen and Bell correlations, and reveals…
Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…
The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be…
Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, and computation. We introduce a graph-based approach to derive classicality inequalities that bound local,…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We consider relations between communication complexity problems and detecting correlations (violating local realism) with no local hidden variable model. We show first universal equivalence between characteristics of protocols used in that…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all…
Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a…
We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the…
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the…
In most Bell tests, the measurement settings are specially chosen so that the maximal quantum violations of the Bell inequalities can be detected, or at least, the violations are strong enough to be observed. Such choices can usually…