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Quantum probability and quantum decision-making.

V I Yukalov1, D Sornette2

  • 1Department of Management, Technology and Economics, ETH Zürich, Swiss Federal Institute of Technology, Zürich 8032, Switzerland Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia yukalov@theor.jinr.ru.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 2, 2015
PubMed
Summary
This summary is machine-generated.

This study defines quantum probability for all measurement types and observables, unifying quantum measurement and decision-making. It outlines conditions for quantum decision theory to align with or diverge from classical theory.

Keywords:
quantum decision-makingquantum measurementsquantum probability

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Area of Science:

  • Quantum Mechanics
  • Probability Theory
  • Decision Theory

Background:

  • Existing definitions of quantum probability are limited in scope.
  • A unified framework for quantum measurements and decision-making is lacking.

Purpose of the Study:

  • To provide a general definition of quantum probability.
  • To establish a common mathematical foundation for quantum measurements and decision-making.
  • To identify conditions for the reduction or necessity of quantum decision theory.

Main Methods:

  • Development of a rigorous general definition of quantum probability.
  • Formulation of conditions for classical and quantum decision theory equivalence.

Main Results:

  • The proposed definition encompasses elementary and composite events, testable and non-testable measurements, and both commuting and non-commuting observables.
  • Quantum measurements and decision-making are unified on a common mathematical footing.
  • Specific conditions are derived for when quantum decision theory simplifies to its classical form or becomes indispensable.

Conclusions:

  • The generalized quantum probability definition offers a comprehensive framework.
  • The unified approach facilitates a deeper understanding of quantum decision processes.
  • The study clarifies the relationship between quantum and classical decision theories.