You're right; maybe I'm overestimating my ability to explain things so that laypeople will understand. But there are some concessions you can make to get the idea across without the full background of complex linear algebra - often I use polarizers as an example, because most people have some experience with them (from sunglasses or 3D movies), and from there it's only a hop, skip, and a jump to entangled photons.
I do try to explain so that people feel like the explanation is totally natural, but then I often run into the problem of people trying to reason about quantum mechanics "in English", so to speak, instead of going to the underlying math to learn more. Any suggestions?
It seems to me that it is easier to get people to realize just that they can't use their regular language to understand what is going on than to actually explain it. People seem to have issues with understanding this primarily because of Dunning-Kruger and because of the large number of popularizations of difficult science that just uses vague analogies.
I'd ask "ok. This is going to take some math. Did you ever take linear algebra?" If yes, then I just explain things. When they answer no (vast majority of the time)I then say "ok do you rem...
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