Experimental Violation of Multiple-Measurement Time-Domain Bell's Inequalities

In the original time-domain Bell's inequalities (Leggett-Garg-type inequalities), the physical objective is measured at three time points. When more time points are chosen, several methods can be used to extend these inequalities. We experimentally demonstrate the violation of these extended inequalities using single photons from a self-assembled quantum dot. In general, for each extension, the quantity by which the quantum-mechanics value exceeds the classical limit becomes larger as the number of measurement time points increases. This quantity has a maximum value for the extensions that have the same number of measurement time points. Furthermore, we evaluate the noise tolerance for these extensions with a quantity that is related to the number of standard deviations by which the experimental result surpasses the classical limit.