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Summary

Description

The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, and none has more extreme values (+/-0.5) at 45, 135, 225, 315 degrees. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows , local realism predicts or less. svg("Bell.svg", width = 7, height = 6)

plot(0, 0, xlim = c(0, 2), ylim = c(-1, 1), type = "n", axes = FALSE, ylab="", xlab = "", mar = c(1, 1, 1, 1))

x <- seq(from = 0, to = 2, length = 181)

lines(x, -cos(pi*x), col = "blue", lwd = 2)

lines(c(0, 1, 2), c(-1, 1, -1), col = "red", lwd = 2)

lines(c(0, 2, 2, 0,0), c(-1, -1, 1, 1, -1))

abline(h=0)

legend(0.05, 0.95, legend = c("Quantum", "Classical"), lwd = c(2, 2), col = c("blue", "red"))

text(c(0, 1/2, 1, 3/2, 2), -0.1, labels = c(0,90, 180, 270, 360), cex = 1.5 )

text(-0.05, c(-1, 0, 1), c(-1, 0, 1), cex=1.5)

text(-0.2, 0, "Correlation", srt = 90, cex = 1.5, pos = 1, xpd = NA)

text( 1.0, -1.1, "Angle between detectors (in degrees)", cex = 1.5, pos = 1, xpd = NA)

graphics.off();
Source Richard Gill, 22 December 2013, drawn with R
Author

Licensing

w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution: Richard Gill, 22 December 2013, drawn with R
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2013-12-23 09:08:43 630× 540× Gill110951 added stars marking correlations found in Bell-CHSH experiments xs <- c(1/4, 3/4, 5/4, 7/4) points(xs, -cos(pi*xs), col = "blue", pch = "*", cex = 2) ys <- c(-1/2, 1/2, 1/2, -1/2) points(xs, ys, col = "red", pch = "*", cex = 2)
2013-12-22 17:48:29 630× 540× Gill110951 improved size and placement of text
2013-12-22 17:27:28 630× 630× Gill110951 Richard Gill, 22 December 2013, drawn with following R script svg("Bell.svg") plot(0, 0, xlim = c(0, 2), ylim = c(-1, 1), type = "n", axes = FALSE, ylab="Correlation", xlab = "Angle between detectors (in degrees)", mar = c(1, 1, 1, 1)) x...

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06b57ed915b8e9a58b3774f906c8ecee1cc3096a

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630 pixel

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Date/TimeThumbnailDimensionsUserComment
current06:13, 31 December 2016Thumbnail for version as of 06:13, 31 December 2016630 × 540 (55 KB)FastilyCloneTransferred from en.wikipedia (MTC!)

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