Violation of contextual generalization of the Leggett-Garg inequality for recognition of ambiguous figures

Abstract

We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality these contexts have the temporal nature and they are given by three pairs of instances of time, $(t_1, t_2), (t_2, t_3), (t_3, t_4),$ where $t_1 < t_2 < t_3.$ We generalize LG conditions of macroscopic realism and noninvasive measurability in the general contextual framework. Our formulation is done in the purely probabilistic terms: existence of the context independent joint probability distribution $P$ and the possibility to reconstruct the experimentally found marginal (two dimensional) probability distributions from the $P.$ We derive an analog of the LG inequality, "contextual LG inequality", and use it as a test of "quantum-likeness" of statistical data collected in a series of experiments on recognition of ambiguous figures. In our experimental study the figure under recognition is the Schroeder stair which is shown with rotations for different angles. Contexts are encoded by dynamics of rotations: clockwise, anticlockwise, and random. Our data demonstrated violation of the contextual LG inequality for some combinations of aforementioned contexts. Since in quantum theory and experiments with quantum physical systems this inequality is violated, e.g., in the form of the original LG-inequality, our result can be interpreted as a sign that the quantum(-like) models can provide a more adequate description of the data generated in the process of recognition of ambiguous figures.