## Analysis of Christensen et al. experiment using Graft's data-files
##
## Christensen, B.G., McCusker, K.T., Altepeter, J.B., Calkins, B.,
## Lim, C.C.W., Gisin, N., and Kwiat, P.G. (2013),
## "Detection-Loophole-Free Test of Quantum Nonlocality, and Applications",
## Phys. Rev. Lett. 111, 130406.
## Donald A. Graft (2014)
## "Analysis of the Christensen et al. Clauser-Horne
## (CH)-Inequality-Based Test of Local Realism",
## http://arxiv.org/abs/1409.5158
## https://pubpeer.com/publications/E0F8384FC19A6034E86D516D03BB38
## Step 3: compute normalized Clauser-Horne B and B'
load("results.RData")
## Total counts, cf. Table 1 of Christensen et al. (2013)
result <- apply(counts, c(1, 2), sum)
t(result[c("SA", "C", "SB", "N"), ])
## count
## setting SA C SB N
## 11 46070 29173 46202 27153018
## 12 48077 34146 146243 28352345
## 21 150837 34473 47448 27827311
## 22 150713 1869 144371 27926988
## Now a separate analysis of each run (sub-experiment)
for (exp in 1:20){
result <- counts[ , , exp, drop = TRUE]
N11 <- result["N", "11"]
C11 <- result["C", "11"]
S11A <- result["SA", "11"]
S11B <- result["SB", "11"]
N12 <- result["N", "12"]
C12 <- result["C", "12"]
S12A <- result["SA", "12"]
S12B <- result["SB", "12"]
N21 <- result["N", "21"]
C21 <- result["C", "21"]
S21A <- result["SA", "21"]
S21B <- result["SB", "21"]
N22 <- result["N", "22"]
C22 <- result["C", "22"]
S22A <- result["SA", "22"]
S22B <- result["SB", "22"]
S1dotA <- S11A + S12A
Sdot1B <- S11B + S21B
N1dot <- N11 + N12
Ndot1 <- N11 + N21
B <- (C11 / N11 + C12 / N12 + C21 / N21) -
(C22 / N22 + S1dotA / N1dot +Sdot1B / Ndot1)
Bprime <- (C11 / N11 + C12 / N12 + C21 / N21 - C22 / N22) /
(S1dotA / N1dot + Sdot1B / Ndot1)
probs11 <- c(C11, S11A - C11, S11B - C11) / N11
coefs11 <- c(1 - N11 / N1dot - N11 / Ndot1, - N11 / N1dot, - N11 / Ndot1)
covmat11 <- diag(probs11) - outer(probs11, probs11)
var11 <- sum(covmat11 * outer(coefs11, coefs11)) / N11
probs12 <- c(C12, S12A - C12) / N12
coefs12 <- c(1 - N12 / N1dot, - N12 / N1dot)
covmat12 <- diag(probs12) - outer(probs12, probs12)
var12 <- sum(covmat12 * outer(coefs12, coefs12)) / N12
probs21 <- c(C21, S21B - C21) / N21
coefs21 <- c(1 - N21 / Ndot1, - N21 / Ndot1)
covmat21 <- diag(probs21) - outer(probs21, probs21)
var21 <- sum(covmat21 * outer(coefs21, coefs21)) / N21
probs22 <- C22 / N22
var22 <- probs22 * (1 - probs22) / N22
seB <- sqrt(var11 + var12 + var21 + var22)
B2 <- sum(probs11 * coefs11) + sum(probs12 * coefs12) + sum(probs21 * coefs21) - probs22
cat("\n", exp, B, seB, B/seB, Bprime)
}
##
## 1 7.693421e-05 5.688486e-05 1.352455 1.023532
## 2 0.0002450607 7.595572e-05 3.226363 1.074909
## 3 -1.172113e-06 6.144997e-05 -0.01907426 0.999638
## 4 9.56839e-05 1.957665e-05 4.887654 1.02834
## 5 -3.793885e-05 3.621009e-05 -1.047742 0.9892583
## 6 4.834904e-05 2.870192e-05 1.684523 1.013973
## 7 7.21832e-05 2.262471e-05 3.190458 1.021118
## 8 4.139045e-05 3.151019e-05 1.313557 1.01225
## 9 3.679404e-05 2.842475e-05 1.294437 1.010616
## 10 9.327091e-05 3.075131e-05 3.033071 1.027717
## 11 2.531185e-05 3.176529e-05 0.7968398 1.007528
## 12 2.118077e-05 2.982078e-05 0.7102688 1.006305
## 13 7.148607e-05 3.169182e-05 2.255663 1.021411
## 14 4.443709e-05 3.466292e-05 1.281978 1.013132
## 15 2.476795e-05 2.573426e-05 0.9624504 1.007367
## 16 4.369174e-05 2.252409e-05 1.939778 1.012766
## 17 6.098904e-05 2.722244e-05 2.240395 1.017868
## 18 6.30766e-05 3.056864e-05 2.063442 1.018499
## 19 4.762152e-05 2.982972e-05 1.596446 1.013618
## 20 3.563453e-05 3.190108e-05 1.117032 1.01064
cat("\nDataSet B se(B) B/se(B) B'")
##
## DataSet B se(B) B/se(B) B'
## Experiments 3 and 5 are anomalous.
## Here are the counts for these two experiments.
## Z is the number of windows with no events at all.
## N is the total number of windows.
## C is the number of windows with coincidences (detections by Alice and by Bob).
## SA and SB are the numbers of windows with detections by Alice and Bob respectively
## (so C is included in both SA and SB).
## So we should have N = Z + SA + SB - C
counts[ , , 3]
## setting
## count 11 12 21 22
## Z 199578 248633 372935 420729
## N 200028 250038 375050 425011
## C 192 285 452 29
## SA 329 409 1961 2245
## SB 313 1281 606 2066
counts[ , , 5]
## setting
## count 11 12 21 22
## Z 1447101 919834 1292416 1311232
## N 1450827 925066 1300120 1325132
## C 1566 1166 1581 82
## SA 2480 1626 7135 7087
## SB 2812 4772 2150 6895