Quantum inferring acausal structures and the Monty Hall problem

TL;DR

This paper introduces a quantum version of the Monty Hall problem using quantum inferring acausal structures, highlighting differences between classical and quantum Bayesian reasoning.

Contribution

It presents a novel quantum formalism for inferring acausal structures and applies it to a quantum Monty Hall scenario, extending Bayesian networks into quantum information theory.

Findings

Quantum structures generalize classical probability distributions.

Quantum Bayesian reasoning differs from classical in the Monty Hall context.

Quantum conditional operators provide a new way to model dependencies.

Abstract

This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of quantum information theory, where density operators are identified with quantum generalization of probability distributions. Conditional relations between quantum counterpart of random variables are described by quantum conditional operators. Presented quantum inferring structures are used to construct a model inspired by scenario of well-known Monty Hall game, where we show the differences between classical and quantum Bayesian reasoning.