Related papers: Platonic Bell inequalities for all dimensions
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have…
The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolved. We determine its exact maximal quantum value and show…
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…
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. The latter has however some…
Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type…
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…
Contemporary versions of Bell's argument against local hidden variable (LHV) theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and various attempts to generalize it. The amount of violation of these inequalities…
The signaling dimension of any given physical system represents its classical simulation cost, that is, the minimum dimension of a classical system capable of reproducing all the input/output correlations of the given system. The signaling…
The precession protocol involves measuring $P_3$, the probability that a uniformly precessing observable (like the position of a harmonic oscillator or a coordinate undergoing spatial rotation) is positive at one of three equally spaced…
We introduce a geometric framework for studying Bell nonlocality in Hilbert space, where, for a given quantum state, nonlocality is quantified by the distance between the state and the set of local states. This approach applies to any Bell…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling…
Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets…
The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett as a mean of testing the quantum mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the…
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through…
Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of state…
Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to…
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…
We derive new tight bipartite Bell inequalities for various scenarios. A bipartite Bell scenario $(X,Y,A,B)$ is defined by the numbers of settings and outcomes per party, $X$, $A$ and $Y$, $B$ for Alice and Bob, respectively. We derive the…
Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint…