Bounding quantum theory with the exclusivity principle in a two-city experiment (original) (raw)

Bell's Inequalities — Foundations and Quantum Communication

Handbook of Natural Computing, 2012

For individual events quantum mechanics makes only probabilistic predictions. Can one go beyond quantum mechanics in this respect? This question has been a subject of debate and research since the early days of the theory. Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hiddenvariable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-thatlight-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind betterthan-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real me aning is, iť

On the EPR paradox and the Bell inequality

In § (1.), after a quick derivation of the Bell inequality which emphasizes where directly unobservable assumptions are introduced, one describes a simple, experimentally realizable, system-apparatus Hamiltonian, for a system of two spin 1/2 particles in singlet state, satisfying the general locality and causality conditions described in § 2 and reproducing the EPR correlations.

Quantum violation of average causal effects in multiple measurement settings

Physical Review A

Estimating causal relations from observed correlations is a central content of science. Although a comprehensive mathematical framework has been developed to identify cause and effect, it is well known that such methods and techniques are not applicable to quantum systems due to Bell's theorem. Generally, the incompatibility between quantum correlation and classical causal theory is illustrated by the violation of Bell inequality. Gachechiladze provides a new method called the violation of lower bound of average causal effect (ACE) to witness the incompatibility. We consider a new lower bound of ACE derived by Cao in multiple measurement settings. We show that there are always pure entangled states and incompatible projective measurements that can generate correlations that violate this new classical lower bound. In Gachechiladze's work, the measurement settings are binary, while the measurement settings in our paper are K-ary (K 2) and we give more general conclusions. When K = 2, the same result as in Gachechiladze's work can be obtained.

Violation of the Bell-CHSH inequality and marginal laws in a single-entity Bell-test experiment

Journal of Mathematical Physics

We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice's and Bob's detection screens, with the measurements' outcomes corresponding to the entity being absorbed or not absorbed in a given time interval. The violation of the marginal laws results from the fact that the choice of the screen on the side of Alice affects the detection probability on the side of Bob, and vice versa, and we show that for certain screen choices, the Bell-CHSH inequality can be violated up to its mathematical maximum. Our analysis provides a clarification of the mechanisms that could be at play when the Bell-CHSH inequality and marginal laws are violated in entangled bipartite systems, which would not primarily depend on the presence of a bipartite structure but on the fact that the latter can manifest as an undivided whole.

An Introduction to Bell's Inequality and its Violation

The application of Bell's Inequality to the questions posed by the famous "EPR Paradox" is reviewed. The emphasis here is on the use of a macroscopic example to develop the inequality and make it more intuitive. We then show how simple quantum mechanical results violate it.

Quantum Violation of Bell’s Inequality: A Misunderstanding Based on a Mathematical Error of Neglect

Journal of Modern Physics, 2021

This paper intends to show how the fabled violation of Bell's inequality by the probabilistic specifications of quantum mechanics derives from a mathematical error, an error of neglect. I have no objection to the probabilities specified by quantum theory, nor to the inequality itself as characterized in the formulation of Clauser, Horne, Shimony, and Holt. Designed to assess consequences of Einstein's principle of local realism, the inequality pertains to a li

On Epr Paradox, Bell's Inequalities and Experiments that Prove Nothing

Old and New Concepts of Physics, 2008

This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experimental results can be explained without such notions. Alternative experiment is proposed to prove the validity of local realism.

Exclusivity principle forbids sets of correlations larger than the quantum set

Physical Review A, 2014

We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments. PACS numbers: 03.65.-w,03.65.Ta, 3.65.Ud