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arXiv:0810.4825

Comment on "Bell Experiment with Genuine Energy-Time Entanglement" by Cabello et al.: Why Franson's Experiment Violates Local Realism

Luiz Carlos Ryff

Published Oct 27, 2008• 0 citations
arXivHTMLPDF

Abstract

It is shown that the model introduced by Cabello et al. to criticize the Franson experiment suffers from the same weakness as the previous model introduced by Aerts et al. with the same purpose. It is also shown why we can assume with confidence that the Franson experiment does violate local realism.
DOI
10.48550/arxiv.0810.4825

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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'.