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Different degrees of freedom of single photons have been entangled and are used as a resource for various quantum technology applications. We present a simple scheme to perform Bell's test and show the violation of CHSH inequality in a…

It is shown that Marinatto's claim [Phys. Rev. Lett. 90, 258901 (2003)] that the proof of "Bell's theorem without inequalities and without probabilities for two observers" [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] requires four…

In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of…

We perform a detailed analysis of the possible violation of various Bell-type inequalities for systems of vector boson-antiboson pairs. Considering the general case of an overall scalar state of the bipartite system, we identify two…

Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard,…

Bell-type experiments that test correlated observables typically involve measurements of spin or polarization on multi-particle systems in singlet states. These observables are all non-commuting and satisfy an uncertainty relation.…

With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…

We emphasize the difficulties of an experiment that can definitely discriminate between local realistic hidden variables theories and quantum mechanics using the Bell CHSH inequalities and a real measurement apparatus. In particular we…

Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's…

Bell inequalities define experimentally observable quantities to detect non-locality. In general, they involve correlation functions of all the parties. Unfortunately, these measurements are hard to implement for systems consisting of many…

The new axiom in set theory, axiom of the empty sets, allows another way to formulate Bell inequality in quantum mechanics. The new axiom emerges from the historical and philosophical analysis of set theory.

(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational…

The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that…

We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes…

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…

This text is an introduction to an operational outlook on Bell inequalities, which has been very fruitful in the past few years. It has lead to the recognition that Bell tests have their own place in applied quantum technologies, because…

The statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.

We show that it is possible to have arbitrarily long sequences of Alices and Bobs so every (Alice, Bob) pair violates a Bell inequality. We propose an experiment to observe this effect with two Alices and two Bobs.

The state of a quantum system, consisting of two distinct subsystems, is called separable if it can be prepared by two distant experimenters who receive instructions from a common source, via classical communication channels. A necessary…

Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…