Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenberg’s uncertainty principle implying the mental state dependence of (in)compatibility of questions

Towards Experiments to Test Violation of the Original Bell Inequality

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser–Horne–Shimony–Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein–Podolsky–Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR–Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound QCHSH = 2√2 to the classical bound CCHSH = 2, i.e., FCHSH = QCHSH/CCHSH = √2 is less than the fraction of the quantum bound for the OB inequality QOB = 3/2 to the classical bound COB = 1, i.e., FOB = QOB/COB = 3/2. Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high

Quantum-like dynamics applied to cognition: a consideration of available options

Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue 'Second quantum revolution: foundational questions'

Perspectives on Correctness in Probabilistic Inference from Psychology

Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making

State entropy and differentiation phenomenon

In the formalism of quantum theory, a state of a system is represented by a density operator . Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy . It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement . To do this, we employ the model of differentiation , where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell’s differentiation, evolution of biological populations, and decision makin

Quantum probability updating from zero priors (by-passing Cromwell’s rule)

Cromwell’s rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes’ rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell’s rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell’s rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell’s rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments

Quantum phenomenology of conjunction fallacy

A quantum-like description of human decision process is developed, and a heuristic argument supporting the theory as sound phenomenology is given. It is shown to be capable of quantitatively explaining the conjunction fallacy in the same footing as the violation of sure-thing principle.Comment: LaTeX 8 pages, 2 figure

Information overload for (bounded) rational agents

Bayesian inference offers an optimal means of processing environmental information and so an advantage in natural selection. We consider the apparent, recent trend in increasing dysfunctional disagreement in e.g. political debate. This is puzzling because Bayesian inference benefits from powerful convergence theorems, precluding dysfunctional disagreement. Information overload is a plausible factor limiting the applicability of full Bayesian inference, but what is the link with dysfunctional disagreement? Individuals striving to be Bayesian-rational, but challenged by information overload, might simplify by using Bayesian Networks or the separation of questions into knowledge partitions, the latter formalized with quantum probability theory. We demonstrate the massive simplification afforded by either approach, but also show how they contribute to dysfunctional disagreement

The specialities of functional condition of heart-vescular system among the schoolchildren with endemic goiter in republic North-Ossetia

Objective: the investigation of thyroid body and haemodynamic characteristics among seniors, living in North-Ossetia Republic. Features and methods: 288 pupils in age of 15 to 17 were examined. We investigated the levels of thyroid-stimulating hormone, free thyroxin, haemodynamic characteristics with the help of expert class hypersonic scanner “Vivid 7 dimeshion" (GE). Results: almost among all pupils was revealed euthyroid condition. The level of TTH hesitated from 0,5 to 2,3 mkMe/ml, didn’t exceeded the normal indexes; the numbers of freeT4 and T3 didn't exceeded normal indexes (11,8 - 21,2 pmole/11,7 - 2,7 nmole/l). Average indexes of morphometric heart indicators, including sizes of heart cavities (EDVLV, ESSLV, ESVLV, EDSLV), thickness index of heart paries (TBPLV, TBBB), retractive ability of myocard (EF. MV) left ventricle were normal among all patients. Striking volume of LV increased not authentically (68.2 ml in comparison with examining group 63.8 ml) remained in normal limits. M V heart indexes, EF and contraction factions were increased without exceeding age indexes in groups with iodine deficit in comparison with examining group. In all two groups were revealed the attributes of connectingtela heart dysplasia. The frequency of mitral seal prolapse was authentically higher in experiment group. In less cases prolapse was holding with an expansion of mitral seal ring and regurgitation of 1 level. The prolapse of tricuspid seal of 1 level with regurgitation of 1 level were observed by far rarely in examining group, but was intense in group with endemic goiter. Conclusion: The necessity of holding prophylactic procedures to hold the correction of available dismicroelements was proved.Цель: изучение функции щитовидной железы и гемодинамических параметров у школьников старших классов, проживающих в республики РСО-Алания. Материалы и методы: обследовано 288 школьника в возрасте от 15 до 17 лет. Исследовали уровни тиреотропного гормона, свободного тироксина, гемодинамические параметры с помощью ультразвукового сканера экспертного класса "Vivid 7 dimeshion” (GE). Результаты: практически у всех школьников было выявлено эутиреоидное состояние. Уровень ТТГ колебался от 0,5 до 2,3 мкМ Е/мл, не превышая нормальные показатели; цифры свТ4 и ТЗ тоже не выходили за пределы нормативов (11,8 - 21,2 пмоль/л. 1,7 - 2,7 нмоль/л соответственно). Средние значения морфометрических показателей сердца, включающие размеры полостей сердца (КД ОЛЖ, КСОЛЖ, КДРЛЖ, КСРЛЖ), толщину стенок сердца (ТЗСЛЖ, ТМЖП), сократительную способность миокарда (ФВ, МО) левого желудочка у всех пациентов были без отклонений от возрастных значений. Ударный объем ЛЖ увеличивался не достоверно (68,2 мл по сравнению с контрольной группой 63,8 мл) оставаясь в пределах нормы. Показатели МО сердца, фракции выброса (сердечного выброса) и фракции укорочения не превышая возрастных значений достоверно, были увеличены в группе с йододефицитом по сравнению с контрольной группой. В обеих группах были выявлены признаки соединительнотканной дисплазии сердца. Частота пролапса митрального клапана была достоверно выше в опытной группе. В меньшем количестве случаев пролапс сопровождался дилатацией кольца митрального клапана и регургитацией 1 степени. Пролапс трикуспидального клапана 1 степени с регургетацией 1 степени наблюдался значительно реже в контрольной группе, но был, значим в группе с эндемическим зобом. Заключение: Доказана необходимость проведения профилактических мероприятий направленных на своевременное выявление и проведение коррекции имеющихся дисмикрозлеметозов