Bell's Theorem and the many experiments that followed allegedly prove that they couldn't have taken on any state before measurement, based on probability theory. If they had predetermined states before you measured them, there is a limit to how often an experiment could yield a certain result. But in these experiments, that limit is exceeded.

Search for "bell inequality".

There are reliable ways to create superposition particles: when you measure in one direction, the other direction is a superposition (https://physics.stackexchange.com/questions/43974/how-can-we...). I have no idea how to create entangled superposition particles: maybe read https://www.eurekalert.org/news-releases/473741.

You can tell the particles are in a superposition because they behave differently than those in a static state:

- Double-split experiment: https://en.wikipedia.org/wiki/Double-slit_experiment - only particles in a superposition create interference patterns

- Bell's paradox: https://www.youtube.com/watch?v=v7jctqKsUMA, https://www.youtube.com/watch?v=hiyKxhETXd8 - entangled particles in a superposition can be measured to make predictions with more confidence than if they were simply static particles with different states

I guess a good search term would be "Polarized light and quantum mechanics" because IMO polarized light is a good example which you can even simulate yourself if you have a polarizing filter (https://www.youtube.com/watch?v=zcqZHYo7ONs&t=736s, https://www.youtube.com/watch?v=ZudziPffS9E, https://chem.libretexts.org/Bookshelves/Physical_and_Theoret...)

The polarised one is really crazy as it is macroscopic and daily life.

It's also dead easy to do - use a cheap laser pointer, a tinfoil cap with a pinhole, and some polarising lenses from an optician (he gave me a couple for free).

This is also my question/confusion.