14 research outputs found
Inconclusive quantum measurements and decisions under uncertainty
We give a mathematical definition for the notion of inconclusive quantum
measurements. In physics, such measurements occur at intermediate stages of a
complex measurement procedure, with the final measurement result being
operationally testable. Since the mathematical structure of Quantum Decision
Theory has been developed in analogy with the theory of quantum measurements,
the inconclusive quantum measurements correspond, in Quantum Decision Theory,
to intermediate stages of decision making in the process of taking decisions
under uncertainty. The general form of the quantum probability for a composite
event is the sum of a utility factor, describing a rational evaluation of the
considered prospect, and of an attraction factor, characterizing irrational,
subconscious attitudes of the decision maker. Despite the involved
irrationality, the probability of prospects can be evaluated. This is
equivalent to the possibility of calculating quantum probabilities without
specifying hidden variables. We formulate a general way of evaluation, based on
the use of non-informative priors. As an example, we suggest the explanation of
the decoy effect. Our quantitative predictions are in very good agreement with
experimental data.Comment: Latex file, 16 page
Quantum Probabilities as Behavioral Probabilities
We demonstrate that behavioral probabilities of human decision makers share
many common features with quantum probabilities. This does not imply that
humans are some quantum objects, but just shows that the mathematics of quantum
theory is applicable to the description of human decision making. The
applicability of quantum rules for describing decision making is connected with
the nontrivial process of making decisions in the case of composite prospects
under uncertainty. Such a process involves deliberations of a decision maker
when making a choice. In addition to the evaluation of the utilities of
considered prospects, real decision makers also appreciate their respective
attractiveness. Therefore, human choice is not based solely on the utility of
prospects, but includes the necessity of resolving the utility-attraction
duality. In order to justify that human consciousness really functions
similarly to the rules of quantum theory, we develop an approach defining human
behavioral probabilities as the probabilities determined by quantum rules. We
show that quantum behavioral probabilities of humans not merely explain
qualitatively how human decisions are made, but they predict quantitative
values of the behavioral probabilities. Analyzing a large set of empirical
data, we find good quantitative agreement between theoretical predictions and
observed experimental data.Comment: Latex file, 32 page
Quantum Probability Theoretic Asset Return Modeling: A Novel Schr\"odinger-Like Trading Equation and Multimodal Distribution
Quantum theory provides a comprehensive framework for quantifying
uncertainty, often applied in quantum finance to explore the stochastic nature
of asset returns. This perspective likens returns to microscopic particle
motion, governed by quantum probabilities akin to physical laws. However, such
approaches presuppose specific microscopic quantum effects in return changes, a
premise criticized for lack of guarantee. This paper diverges by asserting that
quantum probability is a mathematical extension of classical probability to
complex numbers. It isn't exclusively tied to microscopic quantum phenomena,
bypassing the need for quantum effects in returns.By directly linking quantum
probability's mathematical structure to traders' decisions and market
behaviors, it avoids assuming quantum effects for returns and invoking the wave
function. The complex phase of quantum probability, capturing transitions
between long and short decisions while considering information interaction
among traders, offers an inherent advantage over classical probability in
characterizing the multimodal distribution of asset returns.Utilizing Fourier
decomposition, we derive a Schr\"odinger-like trading equation, where each term
explicitly corresponds to implications of market trading. The equation
indicates discrete energy levels in financial trading, with returns following a
normal distribution at the lowest level. As the market transitions to higher
trading levels, a phase shift occurs in the return distribution, leading to
multimodality and fat tails. Empirical research on the Chinese stock market
supports the existence of energy levels and multimodal distributions derived
from this quantum probability asset returns model
Order indices and entanglement production in quantum systems
The review is devoted to two important quantities characterizing many-body
systems, order indices and the measure of entanglement production. Order
indices describe the type of order distinguishing statistical systems. Contrary
to the order parameters characterizing systems in the thermodynamic limit and
describing long-range order, the order indices are applicable to finite systems
and classify all types of orders, including long-range, mid-range, and
short-range orders. The measure of entanglement production quantifies the
amount of entanglement produced in a many-partite system by a quantum
operation. Despite that the notions of order indices and entanglement
production seem to be quite different, there is an intimate relation between
them, which is emphasized in the review.Comment: Latex file, 41 pages, no figure
Evolutionary Processes in Quantum Decision Theory
The review presents the basics of quantum decision theory, with the emphasis
on temporary processes in decision making. The aim is to explain the principal
points of the theory. The difference of an operationally testable rational
choice between alternatives from a choice decorated by irrational feelings is
elucidated. Quantum-classical correspondence is emphasized. A model of quantum
intelligence network is described. Dynamic inconsistencies are shown to be
resolved in the frame of the quantum decision theory.Comment: Latex file, 39 page
A Survey of Quantum-Cognitively Inspired Sentiment Analysis Models
Quantum theory, originally proposed as a physical theory to describe the
motions of microscopic particles, has been applied to various non-physics
domains involving human cognition and decision-making that are inherently
uncertain and exhibit certain non-classical, quantum-like characteristics.
Sentiment analysis is a typical example of such domains. In the last few years,
by leveraging the modeling power of quantum probability (a non-classical
probability stemming from quantum mechanics methodology) and deep neural
networks, a range of novel quantum-cognitively inspired models for sentiment
analysis have emerged and performed well. This survey presents a timely
overview of the latest developments in this fascinating cross-disciplinary
area. We first provide a background of quantum probability and quantum
cognition at a theoretical level, analyzing their advantages over classical
theories in modeling the cognitive aspects of sentiment analysis. Then, recent
quantum-cognitively inspired models are introduced and discussed in detail,
focusing on how they approach the key challenges of the sentiment analysis
task. Finally, we discuss the limitations of the current research and highlight
future research directions