Measurement Models in Quantum Cognition

Miho Fuyama, Andrei Yu. Khrennikov, Masanao Ozawa

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision-making)—quantum-like modelling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects (RREs), cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely, sharp repeatable non-projective measurements — S R P ¯ . This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modelling is not the automatic borrowing of the quantum formalism. Exploring the class S R P ¯ highlights the role of non-commutativity of the state-update maps generated by measurement back action . Thus, ‘non-classicality’ in quantum physics as well as quantum-like modelling for cognition is based on two different types of non-commutativity, of operators (observables) and instruments (state-update maps): observable non-commutativity versus state-update-non-commutativity . We speculate that distinguishing quantum-like properties of the cognitive effects is the expression of the latter, or possibly both. This article is part of the theme issue ‘Quantum theory and topology in models of decision making (Part 1)’.

William H. Batchelder, Hans Colonius, Ehtibar N. Dzhafarov

Hongguang Ma, Binzhou Yan, Ying Qing Mao +1 more

Cognitive bias is an objective existence in cognitive electronic warfare. In this paper, the cognitive bias caused by the measurement error of the electronic reconnaissance system and the cognitive bias of the commander and operator are regarded as quantum superposition states, and the mathematical model of the cognitive bias is established by using quantum cognitive theory, i.e., based on the quantum-like Bayesian network, a framework for inferencing the influence of cognitive bias on situation decision is established, wherein the quantum entanglement factor is defined for describing the relationship of human-machine cognitive biases. By taken the time domain parameter measurement of radar pulse as an example, the cognitive bias is quantitatively analyzed. The experimental results verify the effectiveness of the proposed method. The literature search shows that the proposed method belongs to the first in the field of cognitive electronic warfare, and has a distinct methodological innovation.

E. Conte, Orlando Todarello, Antonio Federici +2 more

Experimental results presented in this paper supports the hypothesis on quantum-like statistical behaviour of cognitive systems (at least human beings). Our quantum-like approach gives the possibility to represent mental states by Hilbert space vectors (complex amplitudes). Such a representation induces huge reduction of information about a mental state. We realize an approach that has no direct relation with reductionist quantum models and we are not interested in statistical behavior of micro systems forming the macro system of the brain. We describe only probabilistic features of cognitive measurements. Our quantum-like approach describes statistics of measurements of cognitive systems with the aim to ascertain if cognitive systems behave as quantum-like systems where here quantum-like cognitive behavior means that cognitive systems result to be very sensitive to changes of the context with regard to the complex of the mental conditions.

Ron Chrisley