QMontyHall {QGameTheory}

Quantum Monty Hall Problem

Description

This function simulates the quantum version of the Monty Hall problem, by taking in Psi_in as the initial quantum state of the game, gamma lying in 0 to pi/2, Ahat and Bhat as the choice operators in SU(3) for Alice and Bob respectively as the inputs. It returns the expected payoffs to Alice and Bob after the end of the game.

Usage

QMontyHall(Psi_in, gamma, Ahat, Bhat)

Arguments

Psi_in

a vector representing the initial quantum state

gamma

a number between 0 and pi/2 including the end points

Ahat

a matrix lying in SU(3)

Bhat

a matrix lying in SU(3)

Value

A vector consisting of the expected payoffs to Alice and Bob as its elements depending on the input parameters.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0109035.pdf

Examples

init()
Psi_in <- kronecker(Q$Qt0, (Q$Qt00+Q$Qt11+Q$Qt22)/sqrt(3))
QMontyHall(Psi_in, pi/4, Q$Identity3, Q$Hhat)