No-Signaling-in-Time Condition for Three-Flavor Neutrino Oscillations

Macrorealism is a fundamental concept in quantum foundations, capturing basic features of our everyday experience. Among the main tools introduced to test violations of macrorealism are the Leggett–Garg inequalities. These inequalities provide necessary and sufficient conditions for a certain data set including the correlators measured in a number of different experimental runs (weak version of macrorealism). Leggett–Garg inequalities have proved useful for detecting violations of macrorealism in neutrino oscillation experiments. However, it is interesting to investigate a set of necessary and sufficient conditions for strong macrorealism—no-signaling-in-time and arrow-of-time conditions—in order to obtain a more complete characterization of macrorealism in the context of neutrino oscillations. In particular, here we extend a previous study of the no-signaling-in-time condition to the case of three-flavor neutrino oscillations, including the CP-violating phase of the Pontecorvo–Maki–Nakagawa–Sakata matrix.