Quantum rational preferences and desirability

TL;DR

This paper extends Bayesian decision theory into the quantum domain, providing a framework for rational preferences over quantum states using Hermitian matrices and expected utility.

Contribution

It introduces a quantum generalization of classical rational preferences, with a representation theorem linking them to quantum expected utility.

Findings

Quantum rational preferences are represented by expected utility over Hermitian matrices.

The theory generalizes classical Bayesian decision-making to quantum settings.

Provides a foundation for quantum decision theory based on axiomatic principles.

Abstract

We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann's axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian matrices. Among other things, this leads us to give a representation theorem showing that quantum complete rational preferences are obtained by means of expected utility considerations.