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Quantum Cognition
Quantum Theory
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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, decision making, human memory,
concepts and conceptual reasoning, human judgment, and perception. 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 or
generalized quantum paradigm or quantum structure paradigm 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), and modeling preferences in decision theory that seem
paradoxical from a traditional rational point of view (e.g., preference reversals).
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.
Main subjects of research
Quantum-like models of information processing ("quantum-like brain")
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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.
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 also supports
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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 for detailed representation of this viewpoint. Quantum mechanics is
fundamentally contextual. 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
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:
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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. But, experimentally,
when subjects are not told the results of the first round, the majority of them
decline to play a second round. 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.
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. 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.
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Human probability judgments
Quantum probability provides a new way to explain human probability
judgment errors including the conjunction and disjunction errors. 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. 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.
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.
Knowledge representation
Concepts are basic cognitive phenomena, which provide the content for
inference, explanation, and language understanding. Cognitive psychology has
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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, and the overextension and underextension of
typicality and membership weight for conjunction and disjunction. 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
 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
 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.
The large amount of data collected by Hampton 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
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explained in terms of contextual interactions, superposition, interference,
entanglement and emergence. 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.
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