It is widely appreciated, due to Bell's theorem, that quantum phenomena are inconsistent with local-realist models. In this context, locality refers to local causality, and there is thus an open possibility for reproducing the quantum predictions with models which internally violate the causal arrow of time, while otherwise adhering to the relevant locality condition. So far, this possibility has been demonstrated only at a toy-model level, and only for systems involving one or two spins (or photons). The present work extends one of these models to quantum correlations between three or more spins which are entangled in the Greenberger-Horne-Zeilinger state.It is widely appreciated, due to Bell's theorem, that quantum phenomena are inconsistent with local-realist models. In this context, locality refers to local causality, and there is thus an open possibility for reproducing the quantum predictions with models which internally violate the causal arrow of time, while otherwise adhering to the relevant locality condition. So far, this possibility has been demonstrated only at a toy-model level, and only for systems involving one or two spins (or photons). The present work extends one of these models to quantum correlations between three or more spins which are entangled in the Greenberger-Horne-Zeilinger state.

Physical Review ASep 12, 20240 citations

Significance of an experiment of the Greenberger-Horne-Zeilinger kind

Henry Pierce Stapp

Restrictive conditions on the class of allowed physical theories are drawn from the assumption that the predictions of quantum theory are valid for an experiment of the kind proposed by Greenberger, Horne, and Zeilinger [in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989)]. It is shown that no theory can be compatible with the following four conditions. (1) The choices to be made by the three experimenters can be treated, in this context, as three independent free variables. (2) For each of the six possible local measurements under consideration, if that local measurement were to be performed, then exactly one of the alternative possible outcomes of this measurement must be selected as the actual outcome. (3) For each triad of measurements in a certain set of possible triads, if that triad were to be performed, then the corresponding triad of selected outcomes must satisfy the correlation condition predicted by quantum theory. (4) For each of the six possible local measurements, if that local measurement were to be performed, then the selected outcome must, according to the theory, be independent of which two experiments will later, in some frame of reference, be performed in the other two regions.Restrictive conditions on the class of allowed physical theories are drawn from the assumption that the predictions of quantum theory are valid for an experiment of the kind proposed by Greenberger, Horne, and Zeilinger [in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989)]. It is shown that no theory can be compatible with the following four conditions. (1) The choices to be made by the three experimenters can be treated, in this context, as three independent free variables. (2) For each of the six possible local measurements under consideration, if that local measurement were to be performed, then exactly one of the alternative possible outcomes of this measurement must be selected as the actual outcome. (3) For each triad of measurements in a certain set of possible triads, if that triad were to be performed, then the corresponding triad of selected outcomes must satisfy the correlation condition predicted by quantum theory. (4) For each of the six possible local measurements, if that local measurement were to be performed, then the selected outcome must, according to the theory, be independent of which two experiments will later, in some frame of reference, be performed in the other two regions.

Physical Review AFeb 1, 199333 citations

Locality and the Greenberger-Horne-Zeilinger Theorem

A. Fahmi, Golshani, M.

In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this Paper, we derive the Greenberger-Horne-Zeilinger type theorem for particles with instantaneous (non-local) interactions at the hidden-variable level. Then, we show that the previous contradiction still exists between quantum mechanics and non-local hidden variable models.In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature of quantum mechanics. In this Paper, we derive the Greenberger-Horne-Zeilinger type theorem for particles with instantaneous (non-local) interactions at the hidden-variable level. Then, we show that the previous contradiction still exists between quantum mechanics and non-local hidden variable models.

arXiv:quant-ph/0608049Aug 6, 20061 citation

Beyond Bell’s theorem: realism and locality without Bell-type correlations

F. De Zela

The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell's theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell's theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.

Scientific ReportsOct 31, 20176 citations

Bell's theorem and beyond

Mark S. Hillery, Bernard Yurke

The authors survey what is known about correlations in physical systems. Bell (1964-6) found that locally realistic theories are limited in the types of correlations which they allow. The more recent results of Greenberger, Horne and Zeilinger (1992) and of Hardy (1989) have shown that local realism imposes even stronger restrictions than those found by Bell. It is less well known that quantum mechanics is also limited in the kinds of correlations it can produce. This was first discovered by Tsirelson (1980). The authors discuss Tsirelson's results and related work by Landau (1987). They conclude by presenting further conditions which quantum mechanical correlations must satisfy.The authors survey what is known about correlations in physical systems. Bell (1964-6) found that locally realistic theories are limited in the types of correlations which they allow. The more recent results of Greenberger, Horne and Zeilinger (1992) and of Hardy (1989) have shown that local realism imposes even stronger restrictions than those found by Bell. It is less well known that quantum mechanics is also limited in the kinds of correlations it can produce. This was first discovered by Tsirelson (1980). The authors discuss Tsirelson's results and related work by Landau (1987). They conclude by presenting further conditions which quantum mechanical correlations must satisfy.

Quantum and Semiclassical Optics Journal of the European Optical Society Part BJun 1, 199519 citations

Critical visibility for N -particle Greenberger-Horne-Zeilinger correlations to violate local realism

Marek Żukowski, Dagomir Kaszlikowski

A sequence of Bell inequalities for $N$ -particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zellinger states, quantum mechanics violates these inequalities by factors exponentially growing with $N$ . The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as ${(2/3)}^{N}$ .A sequence of Bell inequalities for $N$-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zellinger states, quantum mechanics violates these inequalities by factors exponentially growing with $N$. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as ${(2/3)}^{N}$.

Physical Review ASep 1, 199748 citations

A sequence of Bell inequalities for

N

-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zellinger states, quantum mechanics violates these inequalities by factors exponentially growing with

N

. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as

{(2/3)}^{N}