Bell's inequality violation and symmetry

Bell's inequality violation is related to the breakdown of symmetry of photonic field states. The states allowing the violation are characterized by a parameter γ associated with the interaction of the nonlinear medium and radiation. The violation is shown for small values of γ, where the particle aspect of light dominates. The degrading of the entanglement of the beam with increasing γ is discussed. The essential local noncommutativity of the operators involved is obvious.     

Towards a test of non-locality without “supplementary assumptions”

We have experimentally tested the non-local properties of the two-photon states generated by a high brilliance source of entanglement which virtually allows the direct measurement of the full set of photon pairs created by the basic QED process implied by the parametric quantum scattering. Standard Bell measurements and Bell's inequality violation test have been realized over the entire cone of emission of the degenerate pairs. By the same source we have verified Hardy's ladder theory up to the 20th step and the contradiction between the standard quantum theory and the local realism has been tested for 41% of entangled pairs.     

Bell's inequalities,multiphoton states and phase space distributions

The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states (arbitrary number or photons, pure or mixed) of quantised radiation and their violation is connected to other nonclassical properties of the field. Classical states are shown to obey these inequalities and for the family of centered Gaussian states the direct connection between violation of Bell-type inequalities and squeezing is established.     

Three Qubit GHZ Correlations and Generalized Bell Experiments

We present a brief historical introduction to the topic of Bell's theorem. Next we present the surprising features of the three-particle Greenberger—Horne—Zeilinger (GHZ) states. Finally we shall present a method of analysis of the GHZ correlations, which is based on a numerical approach, which is effectively equivalent to the full set of Bell inequalities for correlation functions for the given problem. The aim of our numerical approach is to answer the following question: Do additional possible local settings lead for the GHZ states to more pronounced violation of local realism (measured by the resistance of the quantum nature of the correlations with respect to “white” noise admixtures)?     

Comments on a paper by B. Schulz about Bell's inequalities

Schulz claims to have constructed an actively local stochastic theory which violates Bell's inequality. This is false.     

Complete correlation,detection loophole and Bell's theorem

Two new formulations of Bell's theorem are given here. First, we consider a definite set of two entangled photons with only two polarization directions, for which Bell's locality assumption is violated for the case of perfect correlation. Then, using a different approach, we prove an efficient Bell‐type inequality which is violated by some quantum mechanical predictions, independent of the efficiency factors.     

Detection inefficiencies in Cabello's proof of the three-qubit Bell theorem without inequalities

We consider the loophole due to detector inefficiency in Cabello's argument on Bell's theorem without inequalities for the three-qubit system. It is shown that detectors with low efficiencies can be employed in physical tests. In addition, the mixed states due to the white noise are also considered.     

Locality,Bell's inequality and the GHZ theorem

In this Letter, we have replaced Bell's locality condition by a more general condition which is a special form of non-locality. We use this condition to obtain the Bell inequality and extend our formulation to prove the GHZ theorem.     

Relativistic invariance of Bell's inequality

Based on a simple argument of relativistic covariance, I argue that the correlation between the polarization states of entangled photons, as predicted by quantum mechanics, is Lorentz invariant. Therefore, Bell's inequality for polarization states cannot be affected by the motion of detectors.     

A model with cosmological Bell inequalities

We discuss the possibility of devising cosmological observables which violate Bell's inequalities. Such observables could be used to argue that cosmic scale features were produced by quantum mechanical effects in the very early universe. As a proof of principle, we propose a somewhat elaborate inflationary model where a Bell inequality violating observable can be constructed.     

A new look at Bell's inequalities and Nelson's theorem

In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark about Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on the theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden‐variable model. Finally, we mention that this theory could perhaps be relativistically extended and useful for the formulation of quantum mechanics in curved space‐times.     

Local deterministic description of Einstein-Podolsky-Rosen experiments

We formulate a model of EPR experiments by including variables determining whether a photon will be detected or not. The resulting deterministic model satisfies Bell's original inequality even though it can agree exactly with the quantum mechanical predictions for the performed experiments. It violates variations of the inequality used in the interpretation of the experiments and deduced with the help of additional assumptions.     

Tests of Bell inequalities

According to recent reports, the last loopholes in testing Bell's inequality are closed. It is argued that the really important task in this field has not been tackled yet and that the leading experiments claiming to close locality and detection efficiency loopholes, although making very significant progress, have conceptual drawbacks. The important task is constructing quantum devices which will allow winning games of certain correlated replies against any classical team. A novel game of this type is proposed.     

Generalized quantum measurement

We overcome one of Bell's objections to ‘quantum measurement’ by generalizing the definition to include systems outside the laboratory. According to this definition, a generalized quantum measurement takes place when the value of a classical variable is influenced significantly by an earlier state of a quantum system. A generalized quantum measurement can then take place in equilibrium systems, provided the classical motion is chaotic. This Letter deals with this classical aspect of quantum measurement, assuming that the Heisenberg cut between the quantum dynamics and the classical dynamics is made at a very small scale. For simplicity, a gas with collisions is modelled by an “Arnold gas”.     

p-adic probability distributions of hidden variables

During the last years large interest was shown in p-adic quantum models (especially, in string theory). As usual, new physical models generate new mathematical methods. In our case a new type of stochastics, p-adic stochastics, was arisen inside p-adic quantum physics. We apply this stochastics to propose a justification of the Einstein-Podolsky-Rosen theory of hidden variables, which was in large contradiction with the Bell type inequality. Our main result is the following: if we consider a p-adic probability distribution of hidden variables, then there are no problems with Bell's inequality.