Testing boundaries of applicability of quantum probabilistic formalism to modeling of cognition

TL;DR

This paper explores the limits of quantum probabilistic models in cognition by proposing experimental tests to validate or challenge their applicability, aiming to deepen understanding of quantum-like approaches in psychology.

Contribution

It introduces a novel experimental test inspired by quantum physics to evaluate the applicability of quantum probability models in cognitive science.

Findings

Proposes a cognitive test analogous to the triple-slit experiment.

Aims to confirm or refute the adequacy of quantum probability in cognition.

Opens new avenues for experimental validation of quantum-like models.

Abstract

Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.