Quantum physics violates the basic assumptions of local realism. Particles can be entangled with each other in ways that allow correlations stronger than possible in classical physics. This was first realized by Einstein, Podolsky and Rosen (EPR) in 1935 and led them to conclude that quantum theory was incomplete. It took about 30 years before J. S. Bell found observable consequences of this phenomenon by showing how entangled states violate inequalities for two-particle correlations derived purely from the assumption that the world obeys local realism. Violations of Bell inequalities were first observed experimentally in the Aspect experiment, which will be discussed below. Such experiments are technically challenging and care is needed to avoid any loopholes in the experimental setup that would still permit the description of the experiments by a local realistic theory. Bell inequalities describe violations of local realism on average, meaning that each individual experimental outcome could occur in a local realistic theory. It is the statistics of these outcomes that violates local realism. In contrast, another class of quantum states, so-called Greenberger–Horne–Zeilinger (GHZ) states, which contain three particles, can be shown to violate local realism in each measurement outcome. We will also discuss this class of states and experiments by Zeilinger's group, which demonstrated this type of violation of local realism for the first time. Our aim here is not to discuss the exact relations between quantum entanglement, non-locality and realism, and their physical and philosophical implications. While this is a highly interesting topic which attracts a lot of attention from researchers, such an exploration would go beyond the scope of this book.
Quantum physics violates the basic assumptions of local realism. Particles can be entangled with each other in ways that allow correlations stronger than possible in classical physics. This was first realized by Einstein, Podolsky and Rosen (EPR) in 1935 and led them to conclude that quantum theory was incomplete. It took about 30 years before J. S. Bell found observable consequences of this phenomenon by showing how entangled states violate inequalities for two-particle correlations derived purely from the assumption that the world obeys local realism. Violations of Bell inequalities were first observed experimentally in the Aspect experiment, which will be discussed below. Such experiments are technically challenging and care is needed to avoid any loopholes in the experimental setup that would still permit the description of the experiments by a local realistic theory. Bell inequalities describe violations of local realism on average, meaning that each individual experimental outcome could occur in a local realistic theory. It is the statistics of these outcomes that violates local realism. In contrast, another class of quantum states, so-called Greenberger–Horne–Zeilinger (GHZ) states, which contain three particles, can be shown to violate local realism in each measurement outcome. We will also discuss this class of states and experiments by Zeilinger's group, which demonstrated this type of violation of local realism for the first time. Our aim here is not to discuss the exact relations between quantum entanglement, non-locality and realism, and their physical and philosophical implications. While this is a highly interesting topic which attracts a lot of attention from researchers, such an exploration would go beyond the scope of this book.
Introduction Since its inception, fifty years ago, Bell's theorem has had a long history not only of experimental tests but also of theoretical developments. Studying pairs of correlated quantummechanical particles separated in space, in a composite “entangled” state, Bell [1] showed that the joint ascription of hidden variables and locality to the system led to an inequality that is violated by the predictions of quantum mechanics. Fifteen years later, experiments confirmed the predictions of quantum mechanics, ruling out a large class of local realist theories. One of the most meaningful theoretical developments that followed Bell's work was the Greenberger–Horne–Zeilinger (GHZ) theorem, also known as Bell's theorem without inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who had been working on Bell's theorem since the late 1960s, together with the Austrian physicist Anton Zeilinger, introduced a novelty into the testing of entanglement, extending Bell's theorem in a different and interesting direction. According to Franck Laloë [2], For many years, everyone thought that Bell had basically exhausted the subject by considering all really interesting situations, and that two-spin systems provided the most spectacular quantum violations of local realism. It therefore came as a surprise to many when in 1989 Greenberger, Horne, and Zeilinger (GHZ) showed that systems containing more than two correlated particles may actually exhibit even more dramatic violations of local realism. The trio analyzed the Einstein, Podolsky, and Rosen 1935 argument once again and were able to write what are now called Greenberger–Horne–Zeilinger (GHZ) entangled states, involving three or four correlated spin-1/2 particles, leading to conflicts between local realist theories and quantum mechanics. However, unlike Bell's theorem, the conflict now was not of a statistical nature, as was the case with Bell's theorem, insofar as measurements on a single GHZ state could lead to conflicting predictions with local realistic models [3–5]. In this paper we present the history of the creation of this theorem and analyze its scope.
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.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
"In 1935, Einstein, Podolsky, and Rosen questioned whether quantum mechanics can be complete, as it seemingly does not adhere to a natural view of reality: local realism, which is the notion that an event can only be influenced by events in the past lightcone, and can only influence events in the future lightcone. This question sparked a philosophical debate that lasted for three decades, until John Bell demonstrated that not only are quantum mechanics and local realism philosophically incompatible, but they predict different statistical results for an appropriate set of measurements on entangled particles, which changed the debate to a scientific discussion. Since then, Bell inequality violations have occurred in a plethora of systems, hinting that local realism is indeed wrong. However, every experiment had imperfections that complicated the interpretation --- the experiments had so-called ""loopholes"" which allowed local realism to persist. In this manuscript, we present our work in using optimized sources of entangled photons to perform the long-sought loophole-free Bell test. This landmark experiment invalidates local realism to the best that science will allow. Beyond answering questions on reality, these Bell tests have a important application in generating provably-secure private random numbers, which then can be used as a seed for cryptographic applications. Not only do we demonstrate that nonlocality must exist, but we begin an experimental exploration in an attempt to understand and quantify this nonlocality. We do so by considering all theories that obey no-signaling (or relativistic causality). In our experiments, we observe the counter-intuitive feature of measuring more nonlocality with less entangled states. We also place a bound on the predictive power of any theory that obeys relativistic causality. And finally, we are able to measure quantum correlations only attainable through complex qubits. This work merely begins to probe the quantum boundary, beginning a journey that may someday find evidence of a beyond-quantum theory."
Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.