The Franson interferometer, proposed in 1989 (Franson 1989 Phys. Rev. Lett. 6 2 2205–08 ), beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experiments and Einstein–Podolsky–Rosen (EPR) elements of reality. The mentioned sinusoidal interference pattern is the same as that giving a violation in the usual Bell experiment. Even so, depending on the precise requirements made on the local realist model, this can imply (a) no violation, (b) smaller violation than usual, or (c) full violation of the appropriate statistical bound. Alternatives include (a) using only the measurement outcomes as EPR elements of reality, (b) using the emission time as EPR element of reality, (c) using path realism, or (d) using a modified setup. This paper discusses the nature of these alternatives and how to choose between them. The subtleties of this discussion needs to be taken into account when designing and setting up experiments intended to test local realism. Furthermore, these considerations are also important for quantum communication, for example in Bell-inequality-based quantum cryptography, especially when aiming for device independence. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
The Franson interferometer, proposed in 1989 (Franson 1989 Phys. Rev. Lett. 6 2 2205–08 ), beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experiments and Einstein–Podolsky–Rosen (EPR) elements of reality. The mentioned sinusoidal interference pattern is the same as that giving a violation in the usual Bell experiment. Even so, depending on the precise requirements made on the local realist model, this can imply (a) no violation, (b) smaller violation than usual, or (c) full violation of the appropriate statistical bound. Alternatives include (a) using only the measurement outcomes as EPR elements of reality, (b) using the emission time as EPR element of reality, (c) using path realism, or (d) using a modified setup. This paper discusses the nature of these alternatives and how to choose between them. The subtleties of this discussion needs to be taken into account when designing and setting up experiments intended to test local realism. Furthermore, these considerations are also important for quantum communication, for example in Bell-inequality-based quantum cryptography, especially when aiming for device independence. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
This paper discusses energy-time entanglement experiments and their relation to Einstein-Podolsky-Rosen (EPR) elements of reality.The interferometric experiment proposed by J. D. Franson in 1989 provides the background, and the main issue here is a detailed discussion on whether a Local Realist model can give the Quantum-Mechanical predictions for this setup.The Franson interferometer gives the same interference pattern as the usual Bell experiment (modulo postselection).Even so, depending on the precise requirements made on the Local Realist model, this can imply a) no violation, b) smaller violation than usual, or c) full violation of the appropriate statistical bound.This paper discusses what requirements are necessary on the model to reach a violation, and the motivation for making these requirements.The alternatives include using a) only the measurement outcomes as EPR elements of reality, b) the emission time as EPR element of reality, and c) path realism.The subtleties of this discussion needs to be taken into account when designing and setting up future experiments of this kind, intended to test Local Realism.
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.
Recent experiments on the classic Einstein-Podolsky-Rosen (EPR) setting claim to test the compatibility between nonlocal quantum entanglement and the (special) theory of relativity. Confirmation of quantum theory has led to the interpretation that Einstein's image of physical reality for each photon in the EPR pair cannot be maintained. A detailed critique on two representative experiments is presented following the original EPR notion of local realism. It is argued that relativity does not enter into the picture, however for the Bell-Bohm version of local realism in terms of hidden variables such experiments are significant. Of the two alternatives, namely incompleteness of quantum theory for describing an individual quantum system, and the ensemble view, it is only the former that has been ruled out by the experiments. An alternative approach gives a statistical ensemble interpretation of the observed data, and the significant conclusion that these experiments do not deny physical reality of the photon is obtained. After discussing the need for a photon model, a vortex structure is proposed based on the space-time invariant property-spin, and pure gauge fields. To test the prime role of spin for photons and the angular-momentum interpretation of electromagnetic fields, experimental schemes feasible in modern laboratories are suggested.
"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."
We use the Greenberger-Horne-Zeilinger [in Bell's Theorem, Quantum Theory,and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989)] approach to present three demonstrations of the failure of Einstein-Podolsky-Rosen (EPR) [Phys. Rev. 47, 777 (1935)] local realism for the case of two spinless particles in a two-particle interferometer. The original EPR assumptions of locality and reality do not suffice for this. First, we use the EPR assumptions of locality and reality to establish that in a two-particle interferometer, the path taken by each particle is an element of reality. Second, we supplement the EPR premises by the postulate that when the path taken by a particle is an element of reality, all paths not taken are empty. We emphasize that our approach is not applicable to a single-particle interferometer because there the path taken by the particle cannot be established as an element of reality. We point out that there are real conceptual differences between single-particle, two-particle, and multiparticle interferometry.
We report on a two-photon interference experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)], in which sinusoidal fringes with visibilities greater than 70.7%, such as those predicted by quantum mechanics, violate a Bell inequality. We observe visibility of 80.4\ifmmode\pm\else\textpm\fi{}0.6%, implying a violation of the inequality by 16 standard deviations. Here the elements of reality under consideration are energy and time rather than spin components. Any classical field models describing separate beams in a Franson interferometer are limited to visibilities less than 50%, and hence ruled out as well, without the need for any supplementary assumptions.