Related papers: Groups, Platonic solids and Bell inequalities
Let $G$ be a finite group acting linearly on $\mathbb{R}^n$. A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space $\mathbb{R}^n /\!/G$ as a basic closed semi-algebraic set. We give a new proof of this…
We develop a systematic approach to establish Bell inequalities for qubits based on the Cauchy-Schwarz inequality. We also use the concept of distinct "roots" of Bell function to classify some well-known Bell inequalities for qubits. As…
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality…
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds.
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…
For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…
The temporal Bell inequalities are derived from the assumptions of realism and locality in time. It is shown that quantum mechanics violates these inequalities and thus is in conflict with the two assumptions. This can be used for…
From the beginning of quantum mechanics, there has been a discussion about the concept of reality, as exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced…
Bell inequalities play a central role in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
This letter presents quantum mechanical inequalities which distinguish, for systems of $N$ spin-$\half$ particles ($N>2$), between fully entangled states and states in which at most $N-1$ particles are entangled. These inequalities are…
We derive a single general Bell inequality which is a necessary and sufficient condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle…
Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results.…
We overview series of multiqubit Bell's inequalities which apply to correlation functions. We present conditions that quantum states must satisfy to violate such inequalities.