The origin of Franson-type nonlocal correlation

Franson-type nonlocal correlation results in a second-order intensity fringe between two remotely separated parties via coincidence measurements, whereas the corresponding local measurements show a perfect incoherence feature. This nonlocal correlation fringe between paired photons is mysterious due to the local randomness in both parties. Here, the Franson nonlocal correlation fringe is analytically investigated using the wave nature of photons to understand the mysterious quantum feature. As a result, the nonlocal intensity fringe is turned out to be a measurement selection-based coherence feature, while the local randomness is from effective decoherence among broad bandwidth-distributed photon pairs. As a result, a coherence version of Franson nonlocal correlation is suggested for macroscopic quantum applications with a commercial laser. The local and nonlocal correlations of the proposed scheme show the same results as entangled photon-pair based Franson correlation. At the request of the authors, this article is being retracted effective 28 October 2022.