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Quantum entanglement is often called spooky/surprising/unintuitive, but they key question is to understand why.
To understand that, you have to understand why it is fundamentally impossible for the entangled particle pair be in a predefined state according to experiments done e.g. where one is deterministically yes and the other deterministically down.
In other words, why local hidden-variable theory is not valid.
How to generate entangled particles:
Video 19. Bell's Theorem: The Quantum Venn Diagram Paradox by minutephysics (2017) Source.
Contains the clearest Bell test experiment description seen so far.
It clearly describes the photon-based 22.5, 45 degree/85%/15% probability photon polarization experiment and its result conceptually.
It does not mention spontaneous parametric down-conversion but that's what they likely hint at.
Done in Collaboration with 3Blue1Brown.
Question asking further clarification on why the 100/85/50 thing is surprising:
Video 20. Bell's Inequality I by ViaScience (2014) Source.
Video 21. Quantum Entanglement & Spooky Action at a Distance by Veritasium (2015) Source. Gives a clear explanation of a thought Bell test experiments with electron spin of electron pairs from photon decay with three 120-degree separated slits. The downside is that he does not clearly describe an experimental setup, it is quite generic.
Video 22. Quantum Mechanics: Animation explaining quantum physics by Physics Videos by Eugene Khutoryansky (2013) Source. Usual Eugene, good animations, and not too precise explanations :-) describes a conceptual spin entangled electron-positron pair production Stern-Gerlach experiment as a Bell test experiments. The 85% is mentioned, but not explained at all.
Video 23. Quantum Entanglement: Spooky Action at a Distance by Don Lincoln (2020) Source. This only has two merits compared to Video 21. "Quantum Entanglement & Spooky Action at a Distance by Veritasium (2015)": it mentions the Aspect et al. (1982) Bell test experiment, and it shows the continuous curve similar to But it just does not clearly explain the bell test.
Video 24. Quantum Entanglement Lab by Scientific American (2013) Source. The hosts interview Professor Enrique Galvez of Colgate University who shows briefly the optical table setup without great details, and then moves to a whiteboard explanation. Treats the audience as stupid, doesn't say the keywords spontaneous parametric down-conversion and Bell's theorem which they clearly allude to. You can even them showing a two second footage of the professor explaining the rotation experiments and the data for it, but that's all you get.


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