Metadata-Version: 2.1 Name: Quantum-Correlations-Visualized Version: 0.1.11 Summary: Visual Simulation of a Two-Channel Quantum Bell Test Experiment Author-email: Barry Schwartz Requires-Python: >=3.11 Description-Content-Type: text/plain Classifier: Programming Language :: Python :: 3 Classifier: License :: OSI Approved :: The Unlicense (Unlicense) Classifier: Operating System :: POSIX Classifier: Intended Audience :: Science/Research Classifier: Topic :: Scientific/Engineering :: Visualization Classifier: Topic :: Scientific/Engineering :: Physics Classifier: Environment :: X11 Applications Classifier: Natural Language :: English Requires-Dist: pyglet >= 2.0.9 Project-URL: Author-on-Mastodon, https://masto.ai/@chemoelectric Project-URL: Homepage, https://github.com/chemoelectric/eprb_signal_correlations Visual Simulation of a Two-Channel Quantum Bell Test Experiment --------------------------------------------------------------- Run the program from the command line with something like Quantum-Correlations-Visualized pi/8 Quantum-Correlations-Visualized 3pi/8 Quantum-Correlations-Visualized pi/4 Quantum-Correlations-Visualized 30 Quantum-Correlations-Visualized 60 or run it without an argument to get a usage message. This program simulates in animation an experiment of a kind for which the Nobel Prize in Physics for the year 2022 was in part awarded. A Wikipedia article on this kind of experiment can be found at https://en.wikipedia.org/w/index.php?title=CHSH_inequality&oldid=1173584834 See also https://en.wikipedia.org/w/index.php?title=Bell_test&oldid=1174875317#A_typical_CHSH_(two-channel)_experiment There is a difference, however. In the simulation, the two polarizing beam splitters are rotated continuously on axles, in unison. Also, the photodetectors are able to tell whether the photons they detected were the vertically polarized ones or the horizontally polarized ones. One might suppose this information available as a ‘hidden variable’, if by no other means. In any case, to calculate the correlation coefficient it is necessary to take account of whether the photon was horizontally or vertically polarized, and thus obviously this information is implicitly assumed by quantum mechanics itself. We need the information, so we can estimate the correlation coefficient. The correlation coefficient is estimated by using detection frequencies as stand-ins for probabilities. Various conditional probabilities in this experimental arrangement take forms such as cos²(this)×sin²(that) and so on. Thus one can substitute detection frequencies for these, take square roots, use some algebra and trigonometric identities, and eventually end up calculating an approximation of the ideal value, −cos(2×(phi_2 − phi_1)). A little care has to be taken with quadrants and signs, because there are actually two square roots that are negatives of each other, but otherwise the process is straightforward, if tedious. Before being displayed, the estimated correlation coefficients are passed through a digital lowpass filter with a very low cutoff frequency, so they do not change too rapidly. As for the sense of the correlation coefficient, some will prefer +cos(2×(phi_2 − phi_1)). The sense is arbitrary, as long as it is kept consistent, and then only if one cares about more than just the magnitude of the coefficient. Incidentally, a better way to write the coefficient is −(cos²(phi_2 − phi_1) − sin²(phi_2 − phi_1)) which expresses it in relative intensities of the two polarizing beam splitters, according to the Law of Malus. The correlation coefficient written in this form thus applies almost intuitively to plane-polarized electromagnetic waves. And it is the formula actually used in the program. It is equivalent to the other form via one of the trigonometric double-angle identities found in CRC handbooks and Wikipedia. At the sides of the display are ‘meters’ that show which detectors are detecting what percentage of the horizontally or vertically polarized photons. Thus one has visual confirmation of the correlations, even if the correlation coefficient should seem difficult to interpret. Lines between the ‘meter pointers’ are there to help with seeing the pointers move together, and also just to look pretty. Comments in the source code explain more about the program, such as how the simulation reproduces empirically the correlations predicted by quantum mechanics for a Bell test. The method used might seem novel and surprising.