bet.R

richard — Apr 7, 2014, 7:13 PM

## I use mathematician's notation: theta is the azimuthal angle, phi is the polar 
## (aka zenith) angle; both measured in radians. 
## Reference: https://en.wikipedia.org/wiki/Spherical_coordinates
## Since my measurement directions all lie in equatorial plane I just extract "theta"


AliceDirections <- 
    read.table("http://www.math.leidenuniv.nl/~gill/AliceDirections.txt")

names(AliceDirections) <- c("theta", "phi")

head(AliceDirections) ## N pairs theta, phi (N rows, 2 columns)

       theta    phi
1  0.4558512 1.0748
2  0.5828188 2.0602
3 -0.6764309 0.9770
4  0.0008851 2.4905
5  0.5155671 1.2942
6 -0.1007671 0.7155

NAlice <- nrow(AliceDirections)

NAlice

[1] 100

AliceTheta <- AliceDirections$theta # Alice's azimuthal angles

head(AliceTheta)

[1]  0.4558512  0.5828188 -0.6764309  0.0008851  0.5155671 -0.1007671

BobDirections <- 
    read.table("http://www.math.leidenuniv.nl/~gill/BobDirections.txt")

names(BobDirections) <- c("theta", "phi")

head(BobDirections)

    theta    phi
1  1.4594 2.3205
2  0.5882 2.4816
3 -1.0540 0.8944
4 -0.2971 1.0470
5  1.2251 1.8913
6 -1.1389 2.3236

NBob <- nrow(BobDirections)

NBob

[1] 100

if (NAlice != NBob) print("Error: particle numbers don't match") else
    print("Go ahead!")

[1] "Go ahead!"

BobTheta <- BobDirections$theta  # Bob's azimuthal angles

head(BobTheta)

[1]  1.4594  0.5882 -1.0540 -0.2971  1.2251 -1.1389

## First pair of measurement directions

Alpha <- 0 * pi / 180
Beta <- 45 * pi / 180
A <- sign(cos(AliceTheta - Alpha))
B <- - sign(cos(BobTheta - Beta))
E11 <- mean(A * B)

## Second pair of measurement directions

Alpha <- 0 * pi / 180
Beta <- 135 * pi / 180
A <- sign(cos(AliceTheta - Alpha))
B <- - sign(cos(BobTheta - Beta))
E12 <- mean(A * B)

## Third pair of measurement directions

Alpha <- 90 * pi / 180
Beta <- 45 * pi / 180
A <- sign(cos(AliceTheta - Alpha))
B <- - sign(cos(BobTheta - Beta))
E21 <- mean(A * B)

## Fourth pair of measurement directions

Alpha <- 90 * pi / 180
Beta <- 135 * pi / 180
A <- sign(cos(AliceTheta - Alpha))
B <- - sign(cos(BobTheta - Beta))
E22 <- mean(A * B)

CHSH <- E12 - E11 - E21 - E22

CHSH 

[1] 1.2

if (CHSH > 2.4) print("Congratulations, Joy") else 
    print("Congratulations, Richard")

[1] "Congratulations, Richard"

## Another experiment

AliceTheta <- runif(1000, 0, 360) * pi / 180
BobTheta <- - AliceTheta

Delta <- seq(from = 0, to = 360, by = 10) * pi / 180
Correlation <- numeric(length(Delta))
A <- sign(cos(AliceTheta))
i <- 0
for (delta in Delta) {
    i <- i+1
    B <- - sign(cos(BobTheta - delta))
    Correlation[i] <- mean(A * B)
}
plot(Correlation)