A Quantum Cognition Analysis of the Ellsberg Paradox

The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the 'Allais' and 'Ellsberg paradoxes', in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a 'classical logical' and a 'quantum conceptual', in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.Comment: 11 page

Quantum information in the Posner model of quantum cognition

Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times, especially when in Posner molecules. The spins would serve as biological qubits. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model's quantum-communication ability, we show how it can teleport information incoherently: A state's weights are teleported. Dephasing results from the entangling operation's simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model's operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.Comment: Published versio

Beyond the quantum formalism: consequences of a neural-oscillator model to quantum cognition

In this paper we present a neural oscillator model of stimulus response theory that exhibits quantum-like behavior. We then show that without adding any additional assumptions, a quantum model constructed to fit observable pairwise correlations has no predictive power over the unknown triple moment, obtainable through the activation of multiple oscillators. We compare this with the results obtained in de Barros (2013), where a criteria of rationality gives optimal ranges for the triple moment.Comment: 4 pages; to appear in the Advances in Cognitive Neurodynamics, Proceedings of the 4th International Conference on Cognitive Neurodynamics - 201

Applying Quantum Principles to Psychology

This article starts out with a detailed example illustrating the utility of applying quantum probability to psychology. Then it describes several alternative mathematical methods for mapping fundamental quantum concepts (such as state preparation, measurement, state evolution) to fundamental psychological concepts (such as stimulus, response, information processing). For state preparation, we consider both pure states and densities with mixtures. For measurement, we consider projective measurements and positive operator valued measurements. The advantages and disadvantages of each method with respect to applications in psychology are discussed.Comment: one of the aims of this review paper is to attract attention of experts in quantum information and probability (as well as in quantum foundations) to a new rapidly growing field of applications of quantum theory. The paper establishes the correspondence between concepts of quantum theory and concepts of cognitive science and psychology. Submitted to Physica Script