Experimental violation of Bell's inequality beyond Tsirelson's bound

The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Tsirelson's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.     

Quantum generalizations of Bell's inequality

Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail.     

Bell's inequality forC *-algebras

Bell's inequality dealing with local hidden variables is given two formulations in terms ofC ^*-algebras. In particular, Bell's inequality holds for all states onAB wheneverA andB are unitalC ^*-algebras at least one of which is Abelian, i.e., at least one corresponds to a classical physical system.     

Bell's inequality for a single particle

Bell's inequality must be satisfied by a theory that can be based on local realistic variables. We derive such an inequality and show that it is violated by some quantum mechanical states. These states may be looked upon as pertaining to one particle.This paper is a contribution in honor of Prof. M. Jammer's 80th birthday April 13, 1995.     

Comparison between local Kolmogorovian models and Bell's inequality

The conditions on the relative frequencies of coincidence between the measurements on two physical systems are deduced, in the particular case of four different directions, from Kolmogorovian probability and the Gutkowski and Valdes-Franco computational method. These conditions are compared with those imposed by Bell's inequality. It is proved that Bell's inequality is a necessary but not a sufficient condition for local Kolmogorovian probability. The further assumptions to be added to Bell's inequality, in order to prove the equivalence with local Kolmogorovian probability, are studied. The connection with the results obtained by other authors on the subject is discussed.     

Experimental violation of Bell's inequality in spatial-parity space

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.     

Violation of Bell's inequality with photons from independent sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.     

A remark on Bell's inequality and decomposable normal states

Bell's correlation inequality is considered in the algebraic framework as discussed by Baez. It is shown that all normal states of the tensor product of two W ^*-algebras satisfy Bell's inequality, if and only if every normal state lies in the closure of the convex hull of the normal product states, if and only if one of the algebras is commutative.     

Mean field bound and GHS inequality

A new proof of the mean field bounds for magnetizations is presented. It applies to any single-component spin system which allows GHS inequality, and to anN-vector model forN 3, and to anN-solid sphere model for all values ofN, provided that the interactions are ferromagnetic and translation invariant.     

Has Bell's inequality a general meaning for hidden-variable theories?

We analyze the proof given by J. S. Bell of an inequality between mean values of measurement results which, according to him, would be characteristic of any local hidden-parameter theory. It is shown that Bell's proof is based upon a hypothesis already contained in von Neumann's famous theorem: It consists in the admission that hidden values of parameters must obey the same statistical laws as observed values. This hypothesis contradicts in advance well-known and certainly correct statistical relations in measurement results: One must therefore reject the type of theory considered by Bell, and his inequality has no general meaning.     

Einstein-Podolsky-Rosen paradox,Bell's inequality,and the projection postulate

Our aim is to understand the role of implicit assumptions which has been used by Einstein, Podolsky, and Rosen (EPR) in their famous article [Phys. Rev., 47, 777 (1935)] devoted to the so-called EPR paradox. We found that the projection postulate plays a crucial role in the EPR argument. It seems that EPR made a mistake in this paper — the projection postulate was applied not in its original form (as it has been formulated in von Neumann's book [Mathematical Foundations of Quantum mechanics, Princeton University Press (1955)] but in the form which was later formalized as Lüders' postulate [Ann. Phys., Lpz. 8, 322 (1951)]. Von Neumann's postulate was crucially modified by extending it to observables with degenerate spectra. This modification is the real source of “quantum nonlocality.” The use of the original von Neumann postulate eliminates this problem — instead of (an action at a distance)-nonlocality, we obtain a classical measurement nonlocality, which is related to the synchronization of two measurements (produced on the two parts of a composite system). If one uses correctly von Neumann's projection postulate, no “elements of reality” can be assigned to entangled systems. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

Strong violations of locality by testing Bell's inequality with improved entangled-photon systems

Bell's theorem states that quantum mechanics cannot be accounted for by any local theory. One of the examples is the existence of quantum non-locality is essentially violated by the local Bell's inequality. Therefore, the violation of Bell's inequality(BI) has been regarded as one of the robust evidences of quantum mechanics. Until now, BI has been tested by many experiments, but the maximal violation(i.e., Cirel'son limit) has never been achieved. By improving the design of entangled sources and optimizing the measurement settings, in this work we report the stronger violations of the Clauser–Horne–Shimony–Holt(CHSH)-type Bell's inequality. The biggest value of Bell's function in our experiment reaches √to a significant one: S = 2.772 ± 0.063, approaching to the so-called Cirel'son limit in which the Bell function value is S = 22.Further improvement is possible by optimizing the entangled-photon sources.     

Violation of Bell's inequality by a generalized einstein-podolsky-rosen state using homodyne detection

Using homodyning with weak coherent fields and photon counting, we have observed violations of Bell-type inequalities by the generalized Einstein-Podolsky-Rosen state produced in a pulsed nondegenerate optical parametric amplifier, as predicted by Grangier et al. [Phys. Rev. A 38, 3132 (1988)]. The maximum observed visibility of the interference pattern was (89+/-4)%. This interference can be regarded as a manifestation of nonlocality in the sense described by Banaszek and Wodkiewicz [Phys. Rev. A 58, 4345 (1998)]. We have investigated the interference both theoretically and experimentally and have measured the influence of dispersion and phase matching.     

Entanglement formation and violation of Bell's inequality with a semiconductor single photon source

We report the generation of polarization-entangled photons, using a quantum dot single photon source, linear optics, and photodetectors. Two photons created independently are observed to violate Bell's inequality. The density matrix describing the polarization state of the postselected photon pairs is reconstructed and agrees well with a simple model predicting the quality of entanglement from the known parameters of the single photon source. Our scheme provides a method to create no more than one entangled photon pair per cycle after postselection, a feature useful to enhance quantum cryptography protocols based on shared entanglement.     

On the observability of Bell's inequality violation in the two-atoms optical Stern-Gerlach model

Using the optical Stern-Gerlach model, we have recently shown that the non-local correlations between the internal variables of two atoms that successively interact with the field of an ideal cavity in proximity of a nodal region are affected by the atomic translational dynamics. As a consequence, there can be some difficulties in observing violation of the Bell's inequality for the atomic internal variables. These difficulties persist even if the atoms travel an antinodal region, except when the spatial wave packets are exactly centered in an antinodal point.     

A careful estimation of photon rescatterig in atomic-cascade experimental tests of Bell's inequality

Summary In this paper we show that, in every atomic-cascade experiment performed up to now for testing Bell's inequality, the second photon of the atomic cascade undergoes rescattering with considerable probability. The only experiment of this type in which rescattering is negligible is the Holt and Pipkin's one, but this is also the only experiment whose results grossly violate quantum-mechanical predictions.

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Riassunto Nel presente lavoro si mostra che, in ogni esperimento con cascata atomica realizzato fino ad oggi per indagare la disuguaglianza di Bell, la probabilità che il secondo fotone della cascata atomica subisca rescattering è notevolumente alta. L'unico esperimento del tipo suddetto in cui il rescattering è trascurabile è quello di Holt e Pipkin, ma questo è anche l'unico esperimento i cui risultati sono in netto contrasto con le previsioni quantomeccaniche.

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Резюме В этой статье мы показываем, что в экспериментах по наблюдению атомных каскадов, вьшолненных для проверки неравенства Белла, второй фотон атомного каскада претерпевает перерассеяние с большой вероятностью. Единственный эксперимент этого типа, в котором процесс перерассеяния пренебрежимо мал, является эксперимент Хольта и Пипкина. Но указанный эксперимент, в свою очередь, является единственным экспериментом, результаты которого существенно противоречат предсказаниям квантовой межаники.