Simulated optics experiment/Data analysis: Difference between revisions

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===Introduction===

 

J. Nonlinear Math. Phys. 11 (Supp.) 104–109 (2004).

https://doi.org/10.2991/jnmp.2004.11.s1.13

 

The analysis proceeds as follows.

## Compute <math>\kappa = cos_{LR}^2 - sin_{LR}^2</math>. This is the correlation coefficient for the group, estimated by inference from detection events.

# Designate each of the four correlation coefficients according to which group it is for. The [[#Python|Python example]], for instance, refers to them as <code>kappaL1R1</code>, <code>kappaL1R2</code>, <code>kappaL2R1</code>, and <code>kappaL2R2</code>.

# Display the number of "pulse pair events" that were simulated, the four correlation coefficients, and the estimated CHSH contrast. Also display the theoretical value of the CHSH contrast (<math>2\sqrt{2}\approx{2.828427}</math>) and the difference between the estimated CHSH contrast and the theoretical value. Also display what we will call the ''CHSH violation'': the difference between the estimated CHSH contrast and the number 2. Any value significantly greater than zero seems to be ''supposed to'' mean that the simulation is inherently "quantum mechanical" and involves "instantaneous action at a distance". But you can decide for yourself whether it really means that. Just do the calculations and print them. One should get an estimated CHSH contrast that is close to the theoretical value, and thus a relatively "huge" CHSH violation of about +0.8.

 

* ''[[Simulated optics experiment/Simulator]]''

* E. T. Jaynes, [https://web.archive.org/web/20200915075028/https://bayes.wustl.edu/etj/articles/cmystery.pdf "Clearing up mysteries -- the original goal"] Opening lecture of the eighth International MAXENT Workshop. 1988. This is a classic from the same physicist as the [[wp:Jaynes–Cummings_model|Jaynes-Cummings model]] is named for.

 

=={{header|Julia}}==

kappaL2R2 = compute_correlation_coefficient(anglesL[2], anglesR[2], dataL2R2)

 

 

# The nominal value of the CHSH contrast for the chosen polarizer

 

</pre>

 

=={{header|ObjectIcon}}==

<syntaxhighlight lang="objecticon">

#

# If you run this program as a script, you might get something like

# The u"" is necessary in Object Icon when the string is a Unicode

# string.

angleL1, angleR1, kappaL1R1)

angleL1, angleR2, kappaL1R2)

angleL2, angleR1, kappaL2R1)

angleL2, angleR2, kappaL2R2)

 

# Some might try to object that a CHSH contrast cannot be calculated

# from correlation coefficients computed according to the classical

# classical model can have a CHSH violation, if by fiat you do not

# let a classical model and the classical formulas be used!

Please be aware that one run of that Python program will not produce the same output as another. There are two reasons: (1) the random number generator is seeded randomly, and (2) the simulated devices are running as separate processes. (How Python handles random numbers in a program running as multiple processes I haven't the vaguest idea.)

 

 

<pre>

 

correlation coefs

 

CHSH contrast +2.817493

CHSH violation +0.817493

 

</pre>

 

print()

print(" correlation coefs")

kappaL1R1))

kappaL1R2))

kappaL2R1))

kappaL2R2))

print()

 

correlation coefs

 

CHSH contrast +2.844480

CHSH violation +0.844480

 

</pre>