QDuels_Bob_payoffs {QGameTheory}

Quantum Two Person Duel game

Description

This function returns the expected payoff to Bob for three possible cases for the Quantum Duel game:

1. The game is continued for n rounds and none of the players shoots at the air.

2. The game is continued for 2 rounds and Alice shoots at the air in her second round.

3. The game is continued for 2 rounds and Bob shoots at the air in her second round.

Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuels_Bob_payoffs(Psi, n, a, b, alpha1, alpha2, beta1, beta2)

Arguments

Psi

a vector representing the initial quantum state

n

an integer

a

a number

b

a number

alpha1

a number

alpha2

a number

beta1

a number

beta2

a number

Value

A list consisting of the payoff value to Bob depending on three situations of the quantum duel game: 1) The game is continued for n rounds and none of the players shoots at the air, 2) The game is continued for 2 rounds and Alice shoots at the air in her second round and 3) The game is continued for 2 rounds and Bob shoots at the air in her second round.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
QDuels_Bob_payoffs(Q$Q11, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)
Qs <- (Q$Q0+Q$Q1)/sqrt(2)
Psi <- kronecker(Qs, Qs)
QDuels_Bob_payoffs(Psi, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)