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**Quantum cognition** is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, language, decision making, human memory, concepts and conceptual reasoning, human judgment, and perception.^{ [1] }^{ [2] }^{ [3] }^{ [4] } The field clearly distinguishes itself from the quantum mind as it is not reliant on the hypothesis that there is something micro-physical quantum mechanical about the brain. Quantum cognition is based on the quantum-like paradigm^{ [5] }^{ [6] } or generalized quantum paradigm^{ [7] } or quantum structure paradigm^{ [8] } that information processing by complex systems such as the brain, taking into account contextual dependence of information and probabilistic reasoning, can be mathematically described in the framework of quantum information and quantum probability theory.

- Main subjects of research
- Quantum-like models of information processing ("quantum-like brain")
- Decision making
- Human probability judgments
- Knowledge representation
- Semantic analysis and information retrieval
- Gestalt perception
- History
- Related theories
- See also
- References
- Further reading
- External links

Quantum cognition uses the mathematical formalism of quantum theory to inspire and formalize models of cognition that aim to be an advance over models based on traditional classical probability theory. The field focuses on modeling phenomena in cognitive science that have resisted traditional techniques or where traditional models seem to have reached a barrier (e.g., human memory),^{ [9] } and modeling preferences in decision theory that seem paradoxical from a traditional rational point of view (e.g., preference reversals).^{ [10] } Since the use of a quantum-theoretic framework is for modeling purposes, the identification of quantum structures in cognitive phenomena does not presuppose the existence of microscopic quantum processes in the human brain.^{ [11] }

The brain is definitely a macroscopic physical system operating on the scales (of time, space, temperature) which differ crucially from the corresponding quantum scales. (The macroscopic quantum physical phenomena, such as the Bose-Einstein condensate, are also characterized by the special conditions which are definitely not fulfilled in the brain.) In particular, the brain's temperature is simply too high to be able to perform the real quantum information processing, i.e., to use the quantum carriers of information such as photons, ions, electrons. As is commonly accepted in brain science, the basic unit of information processing is a neuron. It is clear that a neuron cannot be in the superposition of two states: firing and non-firing. Hence, it cannot produce superposition playing the basic role in the quantum information processing. Superpositions of mental states are created by complex networks of neurons (and these are classical neural networks). Quantum cognition community states that the activity of such neural networks can produce effects formally described as interference (of probabilities) and entanglement. In principle, the community does not try to create the concrete models of quantum (-like) representation of information in the brain.^{ [12] }

The quantum cognition project is based on the observation that various cognitive phenomena are more adequately described by quantum information theory and quantum probability than by the corresponding classical theories (see examples below). Thus the quantum formalism is considered an operational formalism that describes nonclassical processing of probabilistic data. Recent derivations of the complete quantum formalism from simple operational principles for representation of information support the foundations of quantum cognition.

Although at the moment we cannot present the concrete neurophysiological mechanisms of creation of the quantum-like representation of information in the brain,^{ [13] } we can present general informational considerations supporting the idea that information processing in the brain matches with quantum information and probability. Here, contextuality is the key word, see the monograph of Khrennikov for detailed representation of this viewpoint.^{ [1] } Quantum mechanics is fundamentally contextual.^{ [14] } Quantum systems do not have objective properties which can be defined independently of measurement context. (As was pointed by N. Bohr, the whole experimental arrangement must be taken into account.) Contextuality implies existence of incompatible mental variables, violation of the classical law of total probability and (constructive and destructive) interference effects. Thus the quantum cognition approach can be considered as an attempt to formalize contextuality of mental processes by using the mathematical apparatus of quantum mechanics.

Suppose a person is given an opportunity to play two rounds of the following gamble: a coin toss will determine whether the subject wins $200 or loses $100. Suppose the subject has decided to play the first round, and does so. Some subjects are then given the result (win or lose) of the first round, while other subjects are not yet given any information about the results. The experimenter then asks whether the subject wishes to play the second round. Performing this experiment with real subjects gives the following results:

- When subjects believe they won the first round, the majority of subjects choose to play again on the second round.
- When subjects believe they lost the first round, the majority of subjects choose to play again on the second round.

Given these two separate choices, according to the *sure thing* principle of rational decision theory, they should also play the second round even if they don't know or think about the outcome of the first round.^{ [15] } But, experimentally, when subjects are not told the results of the first round, the majority of them decline to play a second round.^{ [16] } This finding violates the law of total probability, yet it can be explained as a quantum interference effect in a manner similar to the explanation for the results from double-slit experiment in quantum physics.^{ [2] }^{ [17] }^{ [18] } Similar violations of the sure-thing principle are seen in empirical studies of the Prisoner's Dilemma and have likewise been modeled in terms of quantum interference.^{ [19] }

The above deviations from classical rational expectations in agents’ decisions under uncertainty produce well known paradoxes in behavioral economics, that is, the Allais, Ellsberg and Machina paradoxes.^{ [20] }^{ [21] }^{ [22] } These deviations can be explained if one assumes that the overall conceptual landscape influences the subject's choice in a neither predictable nor controllable way. A decision process is thus an intrinsically contextual process, hence it cannot be modeled in a single Kolmogorovian probability space, which justifies the employment of quantum probability models in decision theory. More explicitly, the paradoxical situations above can be represented in a unified Hilbert space formalism where human behavior under uncertainty is explained in terms of genuine quantum aspects, namely, superposition, interference, contextuality and incompatibility.^{ [23] }^{ [24] }^{ [25] }^{ [18] }

Considering automated decision making, quantum decision trees have different structure compared to classical decision trees. Data can be analyzed to see if a quantum decision tree model fits the data better.^{ [26] }

Quantum probability provides a new way to explain human probability judgment errors including the conjunction and disjunction errors.^{ [27] } A conjunction error occurs when a person judges the probability of a likely event L *and* an unlikely event U to be greater than the unlikely event U; a disjunction error occurs when a person judges the probability of a likely event L to be greater than the probability of the likely event L *or* an unlikely event U. Quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of von Neumann axioms that relax some of the classic Kolmogorov axioms.^{ [28] } The quantum model introduces a new fundamental concept to cognition—the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. Quantum probability provides a simple account of conjunction and disjunction errors as well as many other findings such as order effects on probability judgments.^{ [29] }^{ [30] }^{ [31] }

The liar paradox - The contextual influence of a human subject on the truth behavior of a cognitive entity is explicitly exhibited by the so-called liar paradox, that is, the truth value of a sentence like "this sentence is false". One can show that the true-false state of this paradox is represented in a complex Hilbert space, while the typical oscillations between true and false are dynamically described by the Schrödinger equation.^{ [32] }^{ [33] }

Concepts are basic cognitive phenomena, which provide the content for inference, explanation, and language understanding. Cognitive psychology has researched different approaches for understanding concepts including exemplars, prototypes, and neural networks, and different fundamental problems have been identified, such as the experimentally tested non classical behavior for the conjunction and disjunction of concepts, more specifically the Pet-Fish problem or guppy effect,^{ [34] } and the overextension and underextension of typicality and membership weight for conjunction and disjunction.^{ [35] }^{ [36] } By and large, quantum cognition has drawn on quantum theory in three ways to model concepts.

- Exploit the contextuality of quantum theory to account for the contextuality of concepts in cognition and language and the phenomenon of emergent properties when concepts combine
^{ [11] }^{ [37] }^{ [38] }^{ [39] }^{ [40] } - Use quantum entanglement to model the semantics of concept combinations in a non-decompositional way, and to account for the emergent properties/associates/inferences in relation to concept combinations
^{ [41] } - Use quantum superposition to account for the emergence of a new concept when concepts are combined, and as a consequence put forward an explanatory model for the Pet-Fish problem situation, and the overextension and underextension of membership weights for the conjunction and disjunction of concepts.
^{ [29] }^{ [37] }^{ [38] }

The large amount of data collected by Hampton^{ [35] }^{ [36] } on the combination of two concepts can be modeled in a specific quantum-theoretic framework in Fock space where the observed deviations from classical set (fuzzy set) theory, the above-mentioned over- and under- extension of membership weights, are explained in terms of contextual interactions, superposition, interference, entanglement and emergence.^{ [29] }^{ [42] }^{ [43] }^{ [44] } And, more, a cognitive test on a specific concept combination has been performed which directly reveals, through the violation of Bell's inequalities, quantum entanglement between the component concepts.^{ [45] }^{ [46] }

The research in (iv) had a deep impact on the understanding and initial development of a formalism to obtain semantic information when dealing with concepts, their combinations and variable contexts in a corpus of unstructured documents. This conundrum of natural language processing (NLP) and information retrieval (IR) on the web – and data bases in general – can be addressed using the mathematical formalism of quantum theory. As basic steps, (a) K. Van Rijsbergen introduced a quantum structure approach to IR,^{ [47] } (b) Widdows and Peters utilised a quantum logical negation for a concrete search system,^{ [40] }^{ [48] } and Aerts and Czachor identified quantum structure in semantic space theories, such as latent semantic analysis.^{ [49] } Since then, the employment of techniques and procedures induced from the mathematical formalisms of quantum theory – Hilbert space, quantum logic and probability, non-commutative algebras, etc. – in fields such as IR and NLP, has produced significant results.^{ [50] }

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There are apparent similarities between Gestalt perception and quantum theory. In an article discussing the application of Gestalt to chemistry, Anton Amann writes: "Quantum mechanics does *not* explain Gestalt perception, of course, but in quantum mechanics and Gestalt psychology there exist almost isomorphic conceptions and problems:

- Similarly as with the Gestalt concept, the shape of a quantum object does
*not*a priori exist but it depends on the interaction of this quantum object with the environment (for example: an observer or a measurement apparatus). - Quantum mechanics and Gestalt perception are organized in a holistic way. Subentities do
*not*necessarily exist in a distinct, individual sense. - In quantum mechanics and Gestalt perception
*objects have to be created*by elimination of holistic correlations with the 'rest of the world'."^{ [51] }

Each of the points mentioned in the above text in a simplified manner (Below explanations correlate respectively with the above-mentioned points):

- As an object in quantum physics doesn't have any shape until and unless it interacts with its environment; Objects according to Gestalt perspective do not hold much of a meaning individually as they do when there is a "group" of them or when they are present in an environment.
- Both in quantum mechanics and Gestalt perception, the objects must be studied as a whole rather than finding properties of individual components and interpolating the whole object.
- In Gestalt concept creation of a new object from another previously existing object means that the previously existing object now becomes a sub entity of the new object, and hence "elimination of holistic correlations" occurs. Similarly a new quantum object made from a previously existing object means that the previously existing object looses its holistic view.

Amann comments: "The structural similarities between Gestalt perception and quantum mechanics are on a level of a parable, but even parables can teach us something, for example, that quantum mechanics is more than just production of numerical results or that the Gestalt concept is more than just a silly idea, incompatible with atomistic conceptions."^{ [51] }

Ideas for applying the formalisms of quantum theory to cognition first appeared in the 1990s by Diederik Aerts and his collaborators Jan Broekaert, Sonja Smets and Liane Gabora, by Harald Atmanspacher, Robert Bordley, and Andrei Khrennikov. A special issue on *Quantum Cognition and Decision* appeared in the * Journal of Mathematical Psychology * (2009, vol 53.), which planted a flag for the field. A few books related to quantum cognition have been published including those by Khrennikov (2004, 2010), Ivancivic and Ivancivic (2010), Busemeyer and Bruza (2012), E. Conte (2012). The first Quantum Interaction workshop was held at Stanford in 2007 organized by Peter Bruza, William Lawless, C. J. van Rijsbergen, and Don Sofge as part of the 2007 AAAI Spring Symposium Series. This was followed by workshops at Oxford in 2008, Saarbrücken in 2009, at the 2010 AAAI Fall Symposium Series held in Washington, D.C., 2011 in Aberdeen, 2012 in Paris, and 2013 in Leicester. Tutorials also were presented annually beginning in 2007 until 2013 at the annual meeting of the Cognitive Science Society. A *Special Issue on Quantum models of Cognition* appeared in 2013 in the journal * Topics in Cognitive Science *.

It was suggested by theoretical physicists David Bohm and Basil Hiley that mind and matter both emerge from an "implicate order".^{ [52] } Bohm and Hiley's approach to mind and matter is supported by philosopher Paavo Pylkkänen.^{ [53] } Pylkkänen underlines "unpredictable, uncontrollable, indivisible and non-logical" features of conscious thought and draws parallels to a philosophical movement some call "post-phenomenology", in particular to Pauli Pylkkö's notion of the "aconceptual experience", an unstructured, unarticulated and pre-logical experience.^{ [54] }

The mathematical techniques of both Conte's group and Hiley's group involve the use of Clifford algebras. These algebras account for "non-commutativity" of thought processes (for an example, *see:* noncommutative operations in everyday life).

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However, an area that needs to be investigated is the concept lateralised brain functioning. Some studies in marketing have related lateral influences on cognition and emotion in processing of attachment related stimuli.

**Cognitive psychology** is the scientific study of mental processes such as attention, language use, memory, perception, problem solving, creativity, and reasoning.

**Learning theory** describes how students receive, process, and retain knowledge during learning. Cognitive, emotional, and environmental influences, as well as prior experience, all play a part in how understanding, or a world view, is acquired or changed and knowledge and skills retained.

**Liane Gabora** is a professor of psychology at the University of British Columbia - Okanagan. She is best known for her theory of the "Origin of the modern mind through conceptual closure," which built on her earlier work on "Autocatalytic closure in a cognitive system: A tentative scenario for the origin of culture." Her recent writing on Honing Theory is adding new direction to the considerable work published on theories of creativity.

**Gestalt psychology**, **gestaltism** or **configurationism** is a school of psychology that emerged in the early twentieth century in Austria and Germany as a theory of perception that was a rejection to the basic principles of Wilhelm Wundt's and Edward Titchener's elementalist and structuralist psychology.

In the field of psychology, **cognitive dissonance** occurs when a person holds contradictory beliefs, ideas, or values, and is typically experienced as psychological stress when they participate in an action that goes against one or more of them. According to this theory, when two actions or ideas are not psychologically consistent with each other, people do all in their power to change them until they become consistent. The discomfort is triggered by the person's belief clashing with new information perceived, wherein they try to find a way to resolve the contradiction to reduce their discomfort.

**Decision theory** is the study of an agent's choices. Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes *how* agents actually make the decisions they do.

A **mental model** is an explanation of someone's thought process about how something works in the real world. It is a representation of the surrounding world, the relationships between its various parts and a person's intuitive perception about his or her own acts and their consequences. Mental models can help shape behaviour and set an approach to solving problems and doing tasks.

**Holonomic brain theory**, also known as **The Holographic Brain**, is a branch of neuroscience investigating the idea that human consciousness is formed by quantum effects in or between brain cells. This is opposed by traditional neuroscience, which investigates the brain's behavior by looking at patterns of neurons and the surrounding chemistry, and which assumes that any quantum effects will not be significant at this scale. The entire field of quantum consciousness is often criticized as pseudoscience, as detailed on the main article thereof.

**Computational cognition** is the study of the computational basis of learning and inference by mathematical modeling, computer simulation, and behavioral experiments. In psychology, it is an approach which develops computational models based on experimental results. It seeks to understand the basis behind the human method of processing of information. Early on computational cognitive scientists sought to bring back and create a scientific form of Brentano's psychology.

**Mathematical psychology** is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. Quantifiable behavior is in practice often constituted by task performance.

**Neural binding** is the neuroscientific aspect of what is commonly known as the binding problem: the interdisciplinary difficulty of creating a comprehensive and verifiable model for the unity of consciousness. "Binding" refers to the integration of highly diverse neural information in the forming of one's cohesive experience. The neural binding hypothesis states that neural signals are paired through synchronized oscillations of neuronal activity that combine and recombine to allow for a wide variety of responses to context-dependent stimuli. These dynamic neural networks are thought to account for the flexibility and nuanced response of the brain to various situations. The coupling of these networks is transient, on the order of milliseconds, and allows for rapid activity.

**Concept learning**, also known as **category learning**, **concept attainment**, and **concept formation**, is defined by Bruner, Goodnow, & Austin (1967) as "the search for and listing of attributes that can be used to distinguish exemplars from non exemplars of various categories". More simply put, concepts are the mental categories that help us classify objects, events, or ideas, building on the understanding that each object, event, or idea has a set of common relevant features. Thus, concept learning is a strategy which requires a learner to compare and contrast groups or categories that contain concept-relevant features with groups or categories that do not contain concept-relevant features.

**Decision field theory** (**DFT**) is a dynamic-cognitive approach to human decision making. It is a cognitive model that describes how people actually make decisions rather than a rational or normative theory that prescribes what people should or ought to do. It is also a dynamic model of decision making rather than a static model, because it describes how a person's preferences evolve across time until a decision is reached rather than assuming a fixed state of preference. The preference evolution process is mathematically represented as a stochastic process called a diffusion process. It is used to predict how humans make decisions under uncertainty, how decisions change under time pressure, and how choice context changes preferences. This model can be used to predict not only the choices that are made but also decision or response times.

The **quantum mind** or **quantum consciousness** is a group of hypotheses proposing that classical mechanics cannot explain consciousness. It posits that quantum-mechanical phenomena, such as entanglement and superposition, may play an important part in the brain's function and could explain consciousness.

**José Acacio de Barros** is a Brazilian-American physicist and philosopher with contributions to the foundations of quantum mechanics, quantum cosmology, and quantum cognition. Dr. de Barros received his PhD in Physics from the Centro Brasileiro de Pesquisas Fisicas (CBPF) in 1991 under the supervision of Francisco Antonio Doria and Antonio Fernandes da Fonseca Teixeira. Since 2007 he has been in the Liberal Studies faculty of San Francisco State University. Before going to San Francisco, he was an Associate Professor of Physics at the Federal University at Juiz de Fora, Brazil, and he was a Visiting Associate Professor at the Center for the Study of Language and Information at Stanford University, and has also held visiting positions at the Centro Brasileiro de Pesquisas Fisicas. Dr. de Barros has been a long-term collaborator of Philosopher Patrick Suppes, with whom he published extensively on the foundations of quantum mechanics and joint probabilities. Among his most influential work is his joint research with Nelson Pinto-Neto, in which Bohm's interpretation of quantum mechanics was applied to quantum cosmology, paving the way for bouncing models using realistic interpretation of quantum mechanics. His recent work attempts to give a neurophysiological foundation to quantum-like effects in psychology. He is also among the main proponents, in collaboration with Gary Oas, of the use of negative probabilities to understand quantum systems.

Binocular rivalry is a visual phenomenon wherein one experiences alternating perceptions due to the occurrence of different stimuli presented to the corresponding retinal regions of the two eyes and their competition for perceptual dominance.

**Jerome Robert Busemeyer** is a Distinguished Professor at Indiana University Bloomington in the Department of Psychological & Brain Sciences and Cognitive Science Program.

**Quantum economics** is an emerging research field which applies methods and ideas from quantum physics to the field of economics. It is motivated by the belief that economic processes such as financial transactions have much in common with quantum processes, and can be appropriately modeled using the quantum formalism. It draws on techniques from the related areas of quantum finance and quantum cognition, and is a sub-field of quantum social science.

**Intuitive statistics**, or **folk statistics**, refers to the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline.

**Quantum social science** is an emerging field of interdisciplinary research which draws parallels between quantum physics and the social sciences. Although there is no settled consensus on a single approach, a unifying theme is that, while the social sciences have long modelled themselves on mechanistic science, they can learn much from quantum ideas such as complementarity and entanglement. Some authors are motivated by quantum mind theories that the brain, and therefore human interactions, are literally based on quantum processes, while others are more interested in taking advantage of the quantum toolkit to simulate social behaviours which elude classical treatment. Quantum ideas have been particularly influential in psychology, but are starting to affect other areas such as international relations and diplomacy in what one 2018 paper called a "quantum turn in the social sciences".

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*Word Vectors and Quantum Logic: Experiments with negation and disjunction*. Eighth Mathematics of Language Conference. pp. 141–154. - ↑ Bruza, P. D.; Cole, R. J. (2005). "Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning". In Artemov, S.; Barringer, H.; d'Avila Garcez, A. S.; Lamb, L. C.; Woods, J. (eds.).
*We Will Show Them: Essays in Honour of Dov Gabbay*. College Publications. ISBN 1-904987-11-7. - ↑ Aerts, D. (2009). "Quantum particles as conceptual entities: A possible explanatory framework for quantum theory".
*Foundations of Science*.**14**: 361–411. arXiv: 1004.2530 . doi:10.1007/s10699-009-9166-y. - ↑ Aerts, D.; Broekaert, J.; Gabora, L.; Sozzo, S. (2013). "Quantum structure and human thought".
*Behavioral and Brain Sciences*.**36**(3): 274–276. doi:10.1017/S0140525X12002841. - ↑ Aerts, Diederik; Gabora, Liane; Sozzo, Sandro (September 2013). "Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought".
*Topics in Cognitive Science*.**5**(4): 737–772. arXiv: 1206.1069 . doi:10.1111/tops.12042. PMID 24039114. - ↑ Aerts, D.; Sozzo, S. (2012). "Quantum structures in cognition: Why and how concepts are entangled". In Song, D.; Melucci, M.; Frommholz, I. (eds.).
*Quantum Interaction 2011*. LNCS.**7052**. Berlin: Springer. pp. 116–127. ISBN 978-3-642-24970-9. - ↑ Aerts, D.; Sozzo, S. (2014). "Quantum entanglement in concept combinations".
*International Journal of Theoretical Physics*.**53**: 3587–3603. arXiv: 1302.3831 . doi:10.1007/s10773-013-1946-z. - ↑ Van Rijsbergen, K. (2004).
*The Geometry of Information Retrieval*. Cambridge University Press. ISBN 0-521-83805-3. - ↑ Widdows, D. (2006).
*Geometry and meaning*. CSLI Publications. ISBN 1-57586-448-7. - ↑ Aerts, D.; Czachor, M. (2004). "Quantum aspects of semantic analysis and symbolic artificial intelligence".
*Journal of Physics A*.**37**: L123–L132. arXiv: quant-ph/0309022 . - ↑ Sorah, Michael. "Parserless Extraction; Using a Multidimensional Transient State Vector Machine" (PDF).
- 1 2 Anton Amann: The Gestalt Problem in Quantum Theory: Generation of Molecular Shape by the Environment, Synthese, vol. 97, no. 1 (1993), pp. 125–156, JSTOR 20117832
- ↑ B.J. Hiley:
*Particles, fields, and observers*, Volume I The Origins of Life, Part 1 Origin and Evolution of Life, Section II The Physical and Chemical Basis of Life, pp. 87–106 (PDF) - ↑ Basil J. Hiley, Paavo Pylkkänen:
*Naturalizing the mind in a quantum framework*. In Paavo Pylkkänen and Tere Vadén (eds.): Dimensions of conscious experience, Advances in Consciousness Research, Volume 37, John Benjamins B.V., 2001, ISBN 90-272-5157-6, pages 119–144 - ↑ Paavo Pylkkänen. "Can quantum analogies help us to understand the process of thought?" (PDF).
*Mind & Matter*.**12**(1): 61–91. p. 83–84.

- Busemeyer, J. R.; Bruza, P. D. (2012).
*Quantum models of cognition and decision*. Cambridge University Press. ISBN 978-1-107-01199-1. - Busemeyer, J. R.; Wang, Z. (2019). "Primer on quantum cognition".
*Spanish Journal of Psychology*.**22**. e53. doi:10.1017/sjp.2019.51. - Conte, E. (2012).
*Advances in application of quantum mechanics in neuroscience and psychology: a Clifford algebraic approach*. Nova Science Publishers. ISBN 978-1-61470-325-9. - Ivancevic, V.; Ivancevic, T. (2010).
*Quantum Neural Computation*. Springer. ISBN 978-90-481-3349-9.

- Busemeyer, J. R (2011). "Quantum Cognition and Decision Notes". Indiana University. Archived from the original on October 29, 2011.
Life is complex, it has both real and imaginary parts

- Blutner, Reinhard. "Quantum Cognition".

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