A Simple Quantum Model Linked to Decisions

2019

This study utilises an experiment famous in quantum physics, the Stern-Gerlach experiment, to inform the structure of an experimental protocol from which a quantum cognitive decision model can be developed. The 'quantumness' of this model is tested by computing a discrete quasi-probabilistic Wigner function. Based on theory from quantum physics, our hypothesis is that the Stern-Gerlach protocol will admit negative values in the Wigner function, thus signalling that the cognitive decision model is quantum. A crowdsourced experiment of two images was used to collect decisions around three questions related to image trustworthiness. The resultant data was used to instantiate the quantum model and compute the Wigner function. Negative values in the Wigner functions of both images were encountered, thus substantiating our hypothesis. Findings also revealed that the quantum cognitive model was a more accurate predictor of decisions when compared to predictions computed using Bayes...

Quantum Mechanics, Mathematics, Cognition and Action, 2002

This is what the epistemological universality of quantum mechanics consists of. By no means does it consist, as is often asserted, of the fact that any material system is made of microsystems-which is a physical circumstance, not an epistemological one. The feeling of essentiality conveyed by the quantum mechanical formalism to those who can read it, does not stem from this physical circumstance; it stems exclusively from the universal character of the peculiar cognitive situation dealt with in quantum mechanics. And, while reflections of it are encrypted in the general features of the formalism considered as a whole, this cognitive situation marks also directly the specific formal features that are pointed toward by the expressions "quantum probabilities" and "quantum logic". These simply are not intelligible in terms of what is classically called probabilities and logic. This manifests strikingly that the general epistemological consequences of the quantum mechanical formalism, if elaborated, modify the structure of our classical representations of probabilities and of logic, the two most basic and worked out representations of domains of our everyday thinking and acting. Indeed, when the universal representation of the very first stage of our conceptualization processes, drawn by generalization from quantum mechanics, is injected into classical probabilities and classical logic, they undergo a sort of spectral decomposition; and this places into evidence that, far down beneath language, probabilistic and logical conceptualization merge REMARKS ABOUT THE PROGRAM FOR A FORMALIZED EPISTEMOLOGY *

International Journal of Theoretical Physics, 2014

This work aims to develop a novel BDI agent programming framework, which embeds the reasoning under uncertainty (probabilistic logic) and is capable of a realistic simulation of human reasoning. We claim that such a development can be addressed through the adoption of the mathematical and logical formalism derived from Quantum Mechanics: a scheme fulfilling the necessary requirements is described, useful for both the interpretation of some peculiarities in human behavior, and eventually the adoption of 'quantum computing' formalism for the agent programming. This last possibility could exploit the power of quantum parallelism in practical reasoning applications. Integration with the BDI paradigm enables the straightforward adoption of efficient learning algorithms and procedures, enhancing the behavior and adaptation of the agent to the environment. Int J Theor Phys belonging to those scales and/or conditions, where quantum processes occur. This has led to the formulation of the so called quantum-like [1] and quantum structure paradigms [2], implemented in a few successful studies related mainly to cognitive sciences. Early examples are attempts of explaining observations in the fields of human decision making (violations of the sure thing principle [3], paradoxes emerging from expected utility theories [4], experiments about classification and decision [5]) and probability judgement (conjunction and disjunction fallacies [6, 7], order effects [8], the liar paradox [9], ...). Further investigations have also extended the quantum formalism approach to other cognitive phenomena, such as knowledge representation (invoking different principles of Quantum Mechanics, ranging from superposition [6] to contextuality and interference [10]), information retrieval [11]

Foundations of Science

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing 'fallacies of human reasoning', namely, the 'conjunction fallacy' and the 'disjunction effect'. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of 'emergent reasoning' and 'logical reasoning', where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. 'contextuality', 'emergence', 'entanglement', 'interference' and 'superposition'. As such, it is alternative to the Kahneman-Tversky research programme, which instead aims to explain human fallacies in terms of 'individual heuristics and biases'.

Trends in cognitive sciences, 2015

What type of probability theory best describes the way humans make judgments under uncertainty and decisions under conflict? Although rational models of cognition have become prominent and have achieved much success, they adhere to the laws of classical probability theory despite the fact that human reasoning does not always conform to these laws. For this reason we have seen the recent emergence of models based on an alternative probabilistic framework drawn from quantum theory. These quantum models show promise in addressing cognitive phenomena that have proven recalcitrant to modeling by means of classical probability theory. This review compares and contrasts probabilistic models based on Bayesian or classical versus quantum principles, and highlights the advantages and disadvantages of each approach.

Arxiv preprint arXiv:1107.0237, 2011

We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn [13, 1950], 1953]) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell 1957] proved that in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading.

2020

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum invariance and the nonlocality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for...

In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr's view (the ontic model) and the Einstein's view (the epistemic model).

ETH Research Collection, 2019

The non-extensibility of quantum theory into a theory with improved predictive power is based on a strong assumption of independent free choice, in which the physicists pick a measurement axis independently of anything that couldn't have been caused by their decision. Independent free choice is also at the core of the Nash equilibrium and classical game theory. A more recent line of game-theoretical research based on weakening free choice leads to non-trivial solution concepts with desirable properties such as at-most uniqueness, Pareto optimality, and contextuality. We show how introducing contingent free choice in the foundations of quantum theory yields a class of deterministic and contextual theories with an improved predictive power, and contrast them with the pilot-wave theory. Specifically, we suggest that quantum experiments, such as the EPR experiment , involving measurements located in spacetime, can be recast as dynamic games with imperfect information involving human agents and the universe. The underlying idea is that a physicist picking a measurement axis and the universe picking a measurement outcome are two faces of the same physical contingency phenomenon. The classical, Nashian resolution of these games based on independent free choice is analogous to local hidden variable theories, constrained by the Bell inequalities. On the other hand, in a setup in which agents are rational and omniscient in all possible worlds, under contingent free choice, the Perfectly Transparent Equilibrium provides a contextual resolution, based on the iterated elimination of inconsistent worlds, towards an at-most unique possible world, in which the outcomes of measurements that actually are carried out, and only them, are deterministically defined.

ArXiv Pre-print

In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception and the perceiving subject belong to 'our mental content'. Here we argue that the formalism of quantum theory can be derived from two related intuitive principles: (i) inference is a physical process performed by physical systems, observers, which are part of the experimental setup---this implies non-commutativity and imaginary-time quantum mechanics; (ii) experiments must be described from a first-person perspective---this leads to self-reference, complementarity, and real-time quantum dynamics. This approach sheds new light on the foundations of quantum theory and suggests fundamental equations in physics are typically of second order due to the physical nature of the observer. It also suggests some experimental conjectures: (i) the quantum of action could be understood as the result of the additional energy required to transition from unconscious to conscious perception; (ii) humans can observe a single photon of visible light; (iii) self-aware systems and the neural correlates of the self should be composed of two complementary sub-systems, much like the DNA molecule is composed of two strands---this may help explain the double-hemisphere architecture of the brain. Moreover, this approach may help bridge the gap between science and human experience. We discuss the potential implications of these ideas for the modern research programs on consciousness and contemplative science. As side results: (i) we show that message-passing algorithms and stochastic processes can be written in a quantum-like manner; (ii) we provide evidence that non-stoquasticity, a quantum computational resource, may be related to non-equilibrium phenomena.

2014

Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be bizarre and even ridiculous to apply ideas of quantum physics in order to improve current psychological and linguistic or semantic ideas. However, a closer look shows that there are some parallels in the development of quantum physics and advanced theories of cognitive science dealing with concepts, conceptual composition, vagueness, and prototypicality. In both cases of the historical development, the underlying basic ideas are of geometric nature. In psychology, geometric models of meaning have a long tradition. However, they suffer from many shortcomings which are illustrated by discussing several puzzles of bounded rationality. The main suggestion of the present approach is that geometric models of meaning can be improved by borrowing basic concepts from (von Neumann) quantum theory. In the first part of this article, we consider several puzzles of bounded rationality. These include the Allais-and Ellsberg paradox, the disjunction effect, the conjunction and disjunction fallacies, and question order effects. We argue that the present account of quantum cognition-taking quantum probabilities rather than classical probabilities-can give a more systematic description of these puzzles than the alternate and rather eclectic treatments in the traditional framework of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always and does not automatically provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In the second part of this article, we aim to illustrate how recent progress in the foundation of quantum theory can help to answer the foundational questions of quantum cognition. This includes the opportunity of interpreting the free parameters, which are pure stipulations in the quantum probabilistic framework. Making a careful distinction between foundational and phenomenological research programs, we explain the foundational issue from the perspective of Piron, Foulis, Randall, and others, and we apply it to the foundation of quantum cognition. In this connection, we show that quantum probabilities are of (virtual) conceptual necessity if grounded in an abstract algebraic framework of orthomodular lattices. This framework is motivated by assuming partial Boolean algebras (describing particular perspectives) that are combined into a uniform system while considering certain capacity restrictions. It is at this point that one important aspect of the whole idea of bounded rationality directly enters the theoretical scenery of quantum cognition: resource limitation. Another important aspect of the foundational issue is that it automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of such states. It is possible to relate this formal distinction to the deep conceptual distinction between risk and ignorance. A third outcome is the possibility to identify quantum aspects in dynamic macro-systems using the framework of symbolic dynamics, closely related to the operational perspective of Piron, Foulis, Randall, and others. This helps to understand the ideas of epistemic complementarity and entanglement, and to analyse quantum aspects in third generation neural networks.

American Journal of Physics, 1979

We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.

Journal of Mathematical Psychology, 2009

The subject of this special issue is quantum models of cognition. At first sight it may seem bizarre, even ridiculous, to draw a connection between quantum mechanics, a highly successful theory usually understood as modeling sub-atomic phenomena, and cognitive science. However, a growing number of researchers are looking to quantum theory to circumvent stubborn problems within their own fields. This is also true within cognitive science and related areas, hence this special issue.

International Journal of Theoretical Physics, 2015

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism of quantum theory has provided an efficient resource for modeling these classically problematical situations. In this paper, we start from our successful quantum-theoretic approach to the modeling of concept combinations to formulate a unifying explanatory hypothesis. In it, human reasoning is the superposition of two processes -a conceptual reasoning, whose nature is emergence of new conceptuality, and a logical reasoning, founded on an algebraic calculus of the logical type. In most cognitive processes however, the former reasoning prevails over the latter. In this perspective, the observed deviations from classical logical reasoning should not be interpreted as biases but, rather, as natural expressions of emergence in its deepest form.