Simulated optics experiment/Data analysis: Difference between revisions
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## Compute the following numbers: <math>sin_L = \sqrt{N_{L1}/N}</math>, <math>cos_L = \sqrt{N_{L2}/N}</math>, <math>sin_R = \sqrt{N_{R1}/N}</math>, and <math>cos_R = \sqrt{N_{R2}/N}</math>. These numbers represent an estimate of the orientations of the two beam splitters, by inference from detection events in the light detectors. |
## Compute the following numbers: <math>sin_L = \sqrt{N_{L1}/N}</math>, <math>cos_L = \sqrt{N_{L2}/N}</math>, <math>sin_R = \sqrt{N_{R1}/N}</math>, and <math>cos_R = \sqrt{N_{R2}/N}</math>. These numbers represent an estimate of the orientations of the two beam splitters, by inference from detection events in the light detectors. |
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## Compute <math>cos_{LR} = (cos_R\cdot cos_L) + (sin_R\cdot sin_L)</math> and <math>sin_{LR} = (sin_R\cdot cos_L) - (cos_R\cdot sin_L)</math>. These are angle difference formulas from trigonometry. We are "eliminating the [[wp:Coordinate_system|coordinate system]]". |
## Compute <math>cos_{LR} = (cos_R\cdot cos_L) + (sin_R\cdot sin_L)</math> and <math>sin_{LR} = (sin_R\cdot cos_L) - (cos_R\cdot sin_L)</math>. These are angle difference formulas from trigonometry. We are "eliminating the [[wp:Coordinate_system|coordinate system]]". |
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## Compute <math>\kappa = cos_{LR}^2 - sin_{LR}^2</math>. This is the correlation coefficient for the group. |
## Compute <math>\kappa = cos_{LR}^2 - sin_{LR}^2</math>. This is the correlation coefficient for the group, estimated by inference from detection events. |
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# Designate the four correlation coefficients according to which group |
# 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>. |
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# Compute the estimated CHSH contrast: <code>-kappaL1R1 + kappaL1R2 + kappaL2R2 + kappaL2R2</code>. |
# Compute the estimated CHSH contrast: <code>-kappaL1R1 + kappaL1R2 + kappaL2R2 + kappaL2R2</code>. |
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# 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. |
# 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. |
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