An animation of the CHSH experiment to generate correlated photons is at: http://www.animatedphysics.com/games/photon_longdistance_chsh.htm(adsbygoogle = window.adsbygoogle || []).push({});

@georgir has a program to show the calculations using the formula for photon detection

yields the following for the coincident (same as the animation):return Math.random() < (Math.cos(r(p-a)*2)+1)/2;

classic:

{

"0-22.5": {

"coincident": 1675,

"total": 2501,

"rate": 0.6697321071571372

},

"45-67.5": {

"coincident": 1671,

"total": 2468,

"rate": 0.6770664505672609

},

"45-22.5": {

"coincident": 1709,

"total": 2579,

"rate": 0.6626599457153936

},

"0-67.5": {

"coincident": 820,

"total": 2452,

"rate": 0.33442088091353994

}

}

I am looking for help in calculating the expectation values for the above data. I am interested in adding the expectation values into my animation. A brief explanation on how to do it I found at http://www.gutenberg.us/articles/CHSH_Bell_test:

Any help or checking would be appreciated.

The usual form of the CHSH inequality is:

(1) − 2 ≤ S ≤ 2,

where

(2)S=E(a,b) −E(a,b′) +E(a′, b) +E(a′b′).

aanda′ are detector settings on side A,bandb′ on side B, the four combinations being tested in separate subexperiments. The termsE(a,b) etc. are the quantum correlations of the particle pairs, where the quantum correlation is defined to be the expectation value of the product of the "outcomes" of the experiment, i.e. the statistical average ofA(a)·B(b), whereAandBare the separate outcomes, using the coding +1 for the '+' channel and −1 for the '−' channel.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Adding expectation values to a CHSH animation

Loading...

Similar Threads - Adding expectation values | Date |
---|---|

I Adding types of angular momenta | May 14, 2017 |

Mathematical conundrum when adding complex exponentials | May 22, 2015 |

Quantum imaging with undetected photons - adding of states | Jan 7, 2015 |

Exchange symmetry when adding angular momentum and in LS coupling? | Oct 24, 2014 |

Help on the expectation value of two added operators | Sep 28, 2013 |

**Physics Forums - The Fusion of Science and Community**