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

TL;DR

This paper analyzes the complex relationship between energy-time entanglement experiments, EPR elements of reality, and local realism, highlighting implications for quantum foundations and quantum communication protocols.

Contribution

It clarifies how different assumptions about EPR elements of reality affect Bell inequality violations in energy-time entanglement experiments.

Findings

Sinusoidal interference can imply no violation or full violation of Bell inequalities depending on assumptions.

Different choices of EPR elements of reality lead to varied interpretations of experimental results.

Design considerations for experiments testing local realism are discussed in detail.

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.