In conventional Einstein-Rosen-Podolsky (EPR) experiments that violate local realism, particles are placed in very particular entangled states. We propose here to use two or three spinless Fock-state Bose-Einstein condensates as independent sources in interferometery experiments. While these states do not seem to be entangled, nevertheless we show that interferometers can be constructed that demonstrate a large variety of different violations local reality. We find violations of Bell inequalities, new Greenberger-Horne-Zeilinger (GHZ) contradictions, and Hardy impossibilities. These violations continue to arbitrarily large particle numbers. A necessary condition to observe the quantum effects is that all particles should be observed; if some are missed, the quantum effects disappear.
In conventional Einstein-Rosen-Podolsky (EPR) experiments that violate local realism, particles are placed in very particular entangled states. We propose here to use two or three spinless Fock-state Bose-Einstein condensates as independent sources in interferometery experiments. While these states do not seem to be entangled, nevertheless we show that interferometers can be constructed that demonstrate a large variety of different violations local reality. We find violations of Bell inequalities, new Greenberger-Horne-Zeilinger (GHZ) contradictions, and Hardy impossibilities. These violations continue to arbitrarily large particle numbers. A necessary condition to observe the quantum effects is that all particles should be observed; if some are missed, the quantum effects disappear.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N-body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this Rapid communication, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the Bell-Clauser-Horne-Shimony-Holt inequalities, as well as N-body Hardy impossibilities. With three condensates, we obtain Greenberger-Horne-Zeilinger-type contradictions.
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.
Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell’s failure of local-hiddenvariable (LHV) theories are three historically famous forms of “quantum nonlocality”. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose-Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger-Horne-Zeilinger (GHZ) states, and the ground state of a two-well BEC.
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.
"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."