Bell conditions for local realism are critically revisited. In particular for optical experiments I criticize Bell's proposed response of detectors to signals as extremely idealized. More physical conditions are proposed, whence a realistic local model of an optical experiment is possible which violates the Clauser-Horne (Bell) inequality. The possibility rests on the existence of a coincidence-time loophole in the experiments.
Bell conditions for local realism are critically revisited. In particular for optical experiments I criticize Bell's proposed response of detectors to signals as extremely idealized. More physical conditions are proposed, whence a realistic local model of an optical experiment is possible which violates the Clauser-Horne (Bell) inequality. The possibility rests on the existence of a coincidence-time loophole in the experiments.
In a local realist model, physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described with such a model. Experiments intended to demonstrate a violation usually require additional assumptions that make them vulnerable to a number of ``loopholes.'' In both pulsed and continuously pumped photonic experiments, an experimenter needs to identify which detected photons belong to the same pair, giving rise to the coincidence-time loophole. Here, via two different methods, we derive Clauser-Horne- and Eberhard-type inequalities that are not only free of the fair-sampling assumption (thus not being vulnerable to the detection loophole), but also free of the fair-coincidence assumption (thus not being vulnerable to the coincidence-time loophole). Both approaches can be used for pulsed as well as for continuously pumped experiments. Moreover, as they can also be applied to already existing experimental data, we finally show that a recent experiment [Giustina et al., Nature (London) 497, 227 (2013)] violated local realism without requiring the fair-coincidence assumption.
This chapter begins with a review of the ideas of locality and realism which provide the basis for the Einstein–Podolsky–Rosen paradox. The general conditions defining a local, realistic theory are stated, and then used to prove Bell's theorem, which yields — for any local, realistic theory — an inequality satisfied by certain linear combinations of correlations. It is shown that this inequality is violated by quantum theory and by experiment. The chapter ends with a discussion of possible experimental loopholes and the alternative Greenberger–Horne–Zeilinger (GHZ) state, which would, in principle, make the use of statistical correlations unnecessary.
Abstract. Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or “loopholes ” in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a “loophole-free ” or “definitive ” Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. ar X iv
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or 'loopholes' in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a 'loophole-free' or 'definitive' Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space-time structure in the standard way then quantum mechanics might be consistent with Einstein's local realism. It shows that loopholes are unavoidable in experiments aimed to establish a violation of Bell`s inequalities. We show how the space-time structure can be considered from the contextual point of view. A mathematical framework for the contextual approach is outlined.
Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.