richard — Feb 15, 2014, 11:37 PM
## Gisin and Gisin model
## http://arxiv.org/abs/quant-ph/9905018
## Generate 1 million particle pairs
## Measure them in 20 random pairs of directions
set.seed(4567)
N <- 10^6
z <- runif(N, -1, 1)
t <- runif(N, 0, 2*pi)
r <- sqrt(1 - z^2)
x <- r * cos(t)
y <- r * sin(t)
e <- rbind(x, y, z)
whose <- sample(c(TRUE, FALSE), N, replace=TRUE)
unifs <- runif(N)
for (i in 1:20) {
a <- rnorm(3)
a <- a/sqrt(sum(a^2))
b <- rnorm(3)
b <- b/sqrt(sum(b^2))
ca <- colSums(e*a)
cb <- colSums(e*b)
good <- (unifs < ifelse(whose, abs(ca), abs(cb)))
M <- sum(good)
corr <- sum(sign(ca[good])*sign(cb[good]))/M
print(paste("Experiment ", i, ", actual correlation ", round(sum(a*b),4), ", observed correlation ", round(corr,4)))
}
[1] "Experiment 1 , actual correlation 0.1879 , observed correlation 0.1857"
[1] "Experiment 2 , actual correlation -0.9654 , observed correlation -0.9654"
[1] "Experiment 3 , actual correlation 0.336 , observed correlation 0.3337"
[1] "Experiment 4 , actual correlation -0.8318 , observed correlation -0.8329"
[1] "Experiment 5 , actual correlation 0.7855 , observed correlation 0.7851"
[1] "Experiment 6 , actual correlation -0.8577 , observed correlation -0.8582"
[1] "Experiment 7 , actual correlation -0.9906 , observed correlation -0.9906"
[1] "Experiment 8 , actual correlation -0.6988 , observed correlation -0.6982"
[1] "Experiment 9 , actual correlation -0.9274 , observed correlation -0.9275"
[1] "Experiment 10 , actual correlation -0.1894 , observed correlation -0.1867"
[1] "Experiment 11 , actual correlation -0.7907 , observed correlation -0.7896"
[1] "Experiment 12 , actual correlation 0.3968 , observed correlation 0.3972"
[1] "Experiment 13 , actual correlation 0.5404 , observed correlation 0.5385"
[1] "Experiment 14 , actual correlation -0.3406 , observed correlation -0.3399"
[1] "Experiment 15 , actual correlation 0.6961 , observed correlation 0.6961"
[1] "Experiment 16 , actual correlation -0.2616 , observed correlation -0.2628"
[1] "Experiment 17 , actual correlation 0.5597 , observed correlation 0.5583"
[1] "Experiment 18 , actual correlation -0.8941 , observed correlation -0.8939"
[1] "Experiment 19 , actual correlation 0.576 , observed correlation 0.575"
[1] "Experiment 20 , actual correlation 0.1965 , observed correlation 0.1964"