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.
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.
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'.
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.
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.
Models of a two-photon interference experiment proposed by Franson to study the Einstein-Podolsky-Rosen (EPR) effect are presented. The experiment considers a pair of photons correlated in time and in frequency, each of which is passed through an interferometer. When the path difference through the two interferometers is set so there is no first-order interference, Franson showed that second-order interference between the two photons could occur with 100% visibility. In this paper both quantum and classical models are considered and the importance of the coincidence time window and the effect of the frequency correlation are shown. Calculations are presented for all settings of the interferometers. The EPR effect arises from entangled states; a brief discussion is given of the nature of the entangled state for this type of experiment.
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.
The notion of the Einstein-Podolsky-Rosen (EPR) "element of reality" is much discussed in the literature on the foundations of quantum mechanics. Recently, it has become particularly relevant due to a proposed criterion of the physical reality of a given quantum mechanical observable [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. We examine this proposal and its consequently related measure of non-locality [V. S. Gomez and R. M. Angelo, Phys. Rev. A 97, 012123, (2018)] and argue that the criterion is ill-described as quantifying physical reality without introducing serious inconsistency with the basic notions of realism that under-gird enquiry. We agree that this reality criterion demonstrates, along with the famous GHZ results, that general quantum observable values make for poor elements of reality. However, we also argue that this does not mean no such elements of reality are to be found in quantum theory. By arguing for, and adopting, probability distributions as these elements of reality instead, we demonstrate that the criterion of physical reality is actually one of observable predictability. We then examine the relationship of realism-based non-locality to the Bell form and find that, despite the flawed premise, this measure does indeed codify non-locality that is not captured by Bell inequalities.