Energy-time entanglement, Elements of Reality, and Local Realism

Abstract

The Franson interferometer, proposed in 1989 [J. D. Franson, Phys. Rev. Lett. 62:2205-2208 (1989)], 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.

18 pages, 7 figures, v2 rewritten and extended

References in corpus (5)

• Proposed Bell experiment with genuine energy-time entanglement
• Long-distance distribution of genuine energy-time entanglement
• Experimental Bell inequality violation without the postselection loophole
• Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry
• Minimum detection efficiency for a loophole-free violation of the Braunstein-Caves chained Bell inequalities

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• Quantum interferometers: principles and applications
• Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network
• Certification of genuine time-bin and energy-time entanglement with integrated photonics
• High-Visibility Time-Bin Entanglement for Testing Chained Bell Inequalities
• The future of secure communications: device independence in quantum key distribution
• Boosting energy-time entanglement using coherent time-delayed feedback
• Tight Bounds for the Pearle-Braunstein-Caves Chained Inequality Without the Fair-Coincidence Assumption
• The Franson experiment as an example of spontaneous breaking of time-translation symmetry
• A Sagnac-based arbitrary time-bin state encoder for quantum communication applications
• Unquestionable Bell theorem for interwoven frustrated down conversion processes
• Photonic quantum information with time-bins: Principles and applications