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, 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.
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.
Quantum-like models of information processing ("quantum-like brain")[edit]
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 e.g. the Bose-Einstein condensate are also characterized by the special conditions which are definitely not fulfilled in the brain.) In particular, the brain is simply too hot to be able 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 neural networks of neurons (and these are classical neural networks). Quantum cognition community states that the activity of such neural networks can produce effects which are 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 as an operational formalism describing nonclassical processing of probabilistic data. Recent derivations of the complete quantum formalism from simple operational principles for representation of information supports the foundations of quantum cognition. The subjective probability viewpoint on quantum probability which was developed by C. Fuchs and collaborators [13] also supports the quantum cognition approach, especially using of quantum probabilities to describe the process of decision making.
Although at the moment we cannot present the concrete neurophysiological mechanisms of creation of the quantum-like representation of information in the brain, 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 [1] for detailed representation of this viewpoint. 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.
Decision making[edit]
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:
1) When subjects believe they won the first round, the majority of subjects choose to play again on the second round.
2) When subjects believe they lost the first round, the majority of subjects choose not 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]
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.[18][19][20] 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.[21][22][23]
