Quantum probability and quantum decision making

TL;DR

This paper provides a comprehensive definition of quantum probability applicable to various measurement types and observables, unifying quantum measurement and decision making within a common mathematical framework.

Contribution

It introduces a rigorous, general definition of quantum probability that encompasses both elementary and composite events, enabling a unified approach to quantum measurement and decision making.

Findings

Defines quantum probability for non-commuting observables

Establishes conditions for quantum decision theory to reduce to classical

Framework applicable to operational and inconclusive measurements

Abstract

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.