Quantum Cognition Beyond Hilbert Space I: Fundamentals

TL;DR

This paper introduces an extended quantum-like framework for modeling cognitive phenomena, overcoming previous limitations by representing sequential measurements without relying solely on traditional Hilbert space quantum formalism.

Contribution

It develops an operational, realistic model of human cognition that extends quantum probability beyond Hilbert space, successfully modeling complex cognitive effects.

Findings

Successfully models question order effects

Addresses response replicability issues

Unpacks cognitive effects beyond traditional quantum models

Abstract

The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition paradigm' was recently challenged by its proven impossibility to simultaneously model 'question order effects' and 'response replicability'. In Part I of this paper we describe sequential dichotomic measurements within an operational and realistic framework for human cognition elaborated by ourselves, and represent them in a quantum-like 'extended Bloch representation' where the Born rule of quantum probability does not necessarily hold. In Part II we apply this mathematical framework to successfully model question order effects, response replicability and unpacking effects, thus opening the way toward quantum cognition beyond Hilbert space.