Energy-time entanglement, elements of reality, and local realism

Abstract

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.

High-visibility time-bin entanglement for testing chained Bell inequalities

“…This model fully reproduces the quantum predictions for the time-bin setup. mechanical experiment, as predicted by [4] and experimentally demonstrated by [5]. This is called the postselection loophole [22].…”

“…However, a violation can be obtained [4] by using a generalized, chained Bell-type inequality. Here, we consider N 2 measurements for each observer so that the chained Bell parameter is given by…”

“…In theory, such a chained inequality can provide a strong violation, but was believed [4,5] to be experimentally demanding to the point of being unfeasible. However, in a time-bin experiment, the realism bound is weaker than in a standard Bell experiment (see Appendix A for details) and it is equal to…”

“…As pointed out in several works [2][3][4][5], Franson's scheme suffers from an intrinsic loophole because of the aforementioned postselection. Which events that are discarded could, in principle, be influenced by the measurement settings, and, indeed, a local hidden-variable (LHV) model can reproduce the quantum correlations for the second-order interference exploiting the discarded events [2,3,5,6].…”

A Classical-Light Attack on Energy-Time Entangled Quantum Key Distribution, and Countermeasures

“…as we discussed in section 4.6, the Bell test must always be viewed in the light of loopholes, and the detection loophole has particular consequences for the Franson setup as is shown in publication A [66].…”